Dataset Viewer
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imagewidth (px) 1.14k
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physical_1
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Transfer the pan from the stove top to the counter
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/1/start.jpg
| null |
gemini_example.jpg
|
||
physical_2
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Add coarse salt to the bread in the pan
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/2/start.jpg
| null |
gemini_example.jpg
|
||
physical_3
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Remove the lid from the blue container
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/3/start.jpg
| null |
gemini_example.jpg
|
||
physical_4
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Pick up the bread and place it in the drawer
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/4/start.jpg
| null |
gemini_example.jpg
|
||
physical_5
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Place the tennis ball in the tube
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/5/start.jpg
| null |
gemini_example.jpg
|
||
physical_6
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Stack the pink block on the blue block
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/6/start.jpg
| null |
gemini_example.jpg
|
||
physical_7
|
Given this robotics scene, generate a 10-point end-effector trajectory visualization:
TASK: Upright the tipped-over green mug
FORMAT: Blue circular markers with trajectory labels
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/7/start.jpg
| null |
gemini_example.jpg
|
||
physical_8
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Pour water through the coffee filter
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/8/start.jpg
| null |
gemini_example.jpg
|
||
physical_9
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Add cooking oil to the heated pan
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/9/start.jpg
| null |
gemini_example.jpg
|
||
physical_10
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Transfer shrimp from the orange bowl to the cooking pan
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/10/start.jpg
| null |
gemini_example.jpg
|
||
physical_11
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Place the orange on the white plate
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/11/start.jpg
| null |
gemini_example.jpg
|
||
physical_12
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Put the blue block onto the green car
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/12/start.jpg
| null |
gemini_example.jpg
|
||
physical_13
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Place the white bowl on the cutting board
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/13/start.jpg
| null |
gemini_example.jpg
|
||
physical_14
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Turn the teapot handle to the left
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/14/start.jpg
| null |
gemini_example.jpg
|
||
physical_15
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Stack the orange block on the yellow block
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/15/start.jpg
| null |
gemini_example.jpg
|
||
physical_16
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Place the bread on the empty plate
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/16/start.jpg
| null |
gemini_example.jpg
|
||
physical_17
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Insert the flowers into the white vase
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/17/start.jpg
| null |
gemini_example.jpg
|
||
physical_18
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Place Pikachu in the crate
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/18/start.jpg
| null |
gemini_example.jpg
|
||
physical_19
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Place the beef in the strainer
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/19/start.jpg
| null |
gemini_example.jpg
|
||
physical_20
|
Given this robotics scene in image 1, generate a 10-point end-effector trajectory visualization:
TASK: Flip the egg with the spatula
FORMAT: Blue circular markers with trajectory labels (reference image 2 for style)
REQUIREMENTS:
Start from current end-effector position
End at target completion state
Include intermediate waypoints
Label each point clearly (trajectory1, trajectory2, etc.)
OVERLAY directly on the image. Then, Based on the generated trajectory image, output the corresponding intermediate action sequence with detailed motion primitives.
| Not supported with pagination yet |
embodied
| null |
embodied/20/start.jpg
| null |
gemini_example.jpg
|
||
logical_1
|
Right triangle $ABC$ has one leg of length 6 cm, one leg of length 8 cm and a right angle at $A$. A square has one side on the hypotenuse of triangle $ABC$ and a vertex on each of the two legs of triangle $ABC$. What is the length of one side of the square, in cm? Express your answer as a common fraction.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$120/37$
|
logical/1.jpg
|
logical/rs_1.jpg
| null |
||
logical_2
|
In the given square $ABCD$, the side length is 4 centimeters. $M$ is the midpoint of side $\overline{CD}$. The line segment $\overline{AC}$ intersects the line segment $\overline{BM}$ at point $O$. What is the ratio of the length of $\overline{OC}$ to the length of $\overline{OA}$? Express your answer as a common fraction.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
1/2
|
logical/2.jpg
|
logical/rs_2.jpg
| null |
||
logical_3
|
In a circle with center $O$, $AD$ is a diameter, $ABC$ is a chord, $BO = 5$, and $\angle ABO = \text{arc } CD = 60^\circ$. Find the length of $BC$.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
5
|
logical/3.jpg
|
logical/rs_3.jpg
| null |
||
logical_4
|
Suppose that there are two congruent triangles $\triangle ABC$ and $\triangle ACD$ such that $AB = AC = AD,$ as shown in the following diagram. If $\angle BAC = 20^\circ,$ then what is $\angle BDC$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$10^\circ$
|
logical/4.jpg
|
logical/rs_4.jpg
| null |
||
logical_5
|
Two circles are centered at the origin, as shown. The point $P(8,6)$ is on the larger circle and the point $S(0,k)$ is on the smaller circle. If $QR=3$, what is the value of $k$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
7
|
logical/5.jpg
|
logical/rs_5.jpg
| null |
||
logical_6
|
$ABC$ is an equilateral triangle with sides equal to 2cm. $\overline{BC}$ is extended its own length to $D$, and $E$ is the midpoint of $\overline{AB}$. Suppose $\overline{ED}$ meets $\overline{AC}$ at $F$. Find the area of the quadrilateral $BEFC$ in square centimeters.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$\frac{2\sqrt{3}}{3}$
|
logical/6.jpg
|
logical/rs_6.jpg
| null |
||
logical_7
|
Sector $OAB$ is a quarter of a circle of radius 3 cm. A circle is drawn inside this sector, tangent at three points as shown. What is the number of centimeters in the radius of the inscribed circle? Express your answer in simplest radical form.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$3\sqrt{2}-3$
|
logical/7.jpg
|
logical/rs_7.jpg
| null |
||
logical_8
|
The figure shows two concentric circles. If the length of chord AB is 80 units and chord AB is tangent to the smaller circle, what is the area of the shaded region? Express your answer in terms of π.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
The area of the shaded region is 1600π square units.
|
logical/8.jpg
|
logical/rs_8.jpg
| null |
||
logical_9
|
Let $ABC$ be a triangle with $\angle BAC = 90^\circ$. A circle is tangent to the sides $AB$ and $AC$ at $X$ and $Y$ respectively, such that the points on the circle diametrically opposite $X$ and $Y$ both lie on the side $BC$. Given that $AB = 6$, find the area of the portion of the circle that lies outside the triangle.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$\pi - 2$
|
logical/9.jpg
|
logical/rs_9.jpg
| null |
||
logical_10
|
Circle $T$ has a circumference of $12\pi$ inches, and segment $XY$ is a diameter. If the measure of angle $TXZ$ is $60^{\circ}$, what is the length, in inches, of segment $XZ$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
6
|
logical/10.jpg
|
logical/rs_10.jpg
| null |
||
logical_11
|
The diagram shows 28 lattice points, each one unit from its nearest neighbors. Segment $AB$ meets segment $CD$ at $E$. Find the length of segment $AE$.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$\frac{5\sqrt{5}}{3}$
|
logical/11.jpg
|
logical/rs_11.jpg
| null |
||
logical_12
|
In the diagram, $ABCD$ and $EFGD$ are squares each of area 16. If $H$ is the midpoint of both $BC$ and $EF$, find the total area of polygon $ABHFGD$.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
24
|
logical/12.jpg
|
logical/rs_12.jpg
| null |
||
logical_13
|
$ABCDEFGH$ shown below is a cube. Find $\sin \angle GAC$.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$\frac{\sqrt{3}}{3}$
|
logical/13.jpg
|
logical/rs_13.jpg
| null |
||
logical_14
|
In triangle $ABC$, angle $ACB$ is 50 degrees, and angle $CBA$ is 70 degrees. Let $D$ be the foot of the perpendicular from $A$ to $BC$, $O$ the center of the circle circumscribed about triangle $ABC$, and $E$ the other end of the diameter which goes through $A$. Find the angle $DAE$, in degrees.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
The angle $DAE$ is $20^\circ$.
|
logical/14.jpg
|
logical/rs_14.jpg
| null |
||
logical_15
|
In $\triangle ABC$ lines $CE$ and $AD$ are drawn so that $\dfrac{CD}{DB}=\dfrac{3}{1}$ and $\dfrac{AE}{EB}=\dfrac{3}{2}$. Let $r=\dfrac{CP}{PE}$ where $P$ is the intersection point of $CE$ and $AD$. Then $r$ equals:
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
The final calculated value for r is 5.
|
logical/15.jpg
|
logical/rs_15.jpg
| null |
||
logical_16
|
The triangle shown is an equilateral triangle with side length 12 cm. A side of the triangle is the diameter of the circle. If the sum of the areas of the two small shaded regions in square centimeters in simplest radical form is $a\pi - b\sqrt{c}$, what is $a+b+c$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
33
|
logical/16.jpg
|
logical/rs_16.jpg
| null |
||
logical_17
|
In the adjoining figure, , $CD$ is the diameter of a semicircle with center $O$. Point $A$ lies on the extension of $DC$ past $C$; point $E$ lies on the semicircle, and $B$ is the point of intersection (distinct from $E$) of line segment $AE$ with the semicircle. If length $AB$ equals length $OD$, and the measure of $\angle EOD$ is $45^\circ$, then find the measure of $\angle BAO$, in degrees.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$15^\circ$
|
logical/17.jpg
|
logical/rs_17.jpg
| null |
||
logical_18
|
In $\triangle ABC$ points $D$ and $E$ lie on $\overline{BC}$ and $\overline{AC}$, respectively. The diagram below illustrates the setup. If $\overline{AD}$ and $\overline{BE}$ intersect at $T$ so that $AT/DT=3$ and $BT/ET=4$, what is $CD/BD$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
4/11
|
logical/18.jpg
|
logical/rs_18.jpg
| null |
||
logical_19
|
In the diagram below , $WXYZ$ is a trapezoid such that $\overline{WX}\parallel \overline{ZY}$ and $\overline{WY}\perp\overline{ZY}$. If $YZ = 12$, $\tan Z = 1.5$, and $\tan X = 2$, then what is $XY$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$9\sqrt{5}$
|
logical/19.jpg
|
logical/rs_19.jpg
| null |
||
logical_20
|
An isosceles right triangle is removed from each corner of a square piece of paper, as shown, to create a rectangle. If $AB = 12$ units, what is the combined area of the four removed triangles, in square units?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
72
|
logical/20.jpg
|
logical/rs_20.jpg
| null |
||
logical_21
|
In triangle $ABC$, $AB = 11$, $AC = 13$, and $BC = 20$. The medians $AD$, $BE$, and $CF$ of triangle $ABC$ intersect at the centroid $G$. Let $P$ be the foot of the altitude from $G$ to $BC$. Find $GP$.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$\frac{11}{5}$
|
logical/21.jpg
|
logical/rs_21.jpg
| null |
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logical_22
|
In the figure, , $PA$ is tangent to semicircle $SAR$, $PB$ is tangent to semicircle $RBT$, and $SRT$ is a straight line. If arc $AS$ is $58^\circ$ and arc $BT$ is $37^\circ$, then find $\angle APB$, in degrees.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
The value of $\angle APB$ is $95^\circ$.
|
logical/22.jpg
|
logical/rs_22.jpg
| null |
||
logical_23
|
In the diagram, , $AB = 13\text{ cm},$ $DC = 20\text{ cm},$ and $AD = 5\text{ cm}.$ What is the length of $AC,$ to the nearest tenth of a centimeter?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
The length of $AC,$ to the nearest tenth of a centimeter, is $24.2\text{ cm}.$
|
logical/23.jpg
|
logical/rs_23.jpg
| null |
||
logical_24
|
What is the ratio of the area of the shaded square to the area of the large square? (The figure is drawn to scale.)
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
1/8
|
logical/24.jpg
|
logical/rs_24.jpg
| null |
||
logical_25
|
The orthocenter of triangle $ABC$ divides altitude $\overline{CF}$ into segments with lengths $HF = 6$ and $HC = 15.$ Calculate $\tan A \tan B.$
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
| Not supported with pagination yet |
logical
|
$\frac{7}{2}$
|
logical/25.jpg
|
logical/rs_25.jpg
| null |
||
logical_26
|
In triangle $ABC,$ the side lengths are $a = 7,$ $b = 9,$ and $c = 4.$ The incenter $I$ is shown in the diagram below.
The position vector of the incenter can be expressed as a weighted average of the position vectors of the vertices:
\[\overrightarrow{I} = x \overrightarrow{A} + y \overrightarrow{B} + z \overrightarrow{C},\]
where $x, y,$ and $z$ are constants such that $x + y + z = 1.$ Find the ordered triple $(x,y,z).$
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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$\left( \frac{7}{20}, \frac{9}{20}, \frac{1}{5} \right)$
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logical_27
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A square with side length 1 is rotated about one vertex by an angle of $\alpha,$ where $0^\circ < \alpha < 90^\circ$ and $\cos \alpha = \frac{4}{5}.$ Find the area of the shaded region that is common to both squares.
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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The area of the shaded region that is common to both squares is $\frac{1}{2}.$
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logical_28
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In the figure, $ABCD$ and $BEFG$ are squares, and $BCE$ is an equilateral triangle. What is the number of degrees in angle $GCE$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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The number of degrees in angle $GCE$ is $45^\circ$.
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logical/rs_28.jpg
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logical_29
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What is the area in square units of the quadrilateral XYZW shown below?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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The area of the quadrilateral XYZW is 2304 square units.
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logical/29.jpg
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logical/rs_29.jpg
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logical_30
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Let $ABCD$ be a parallelogram. $M$ is the midpoint of $AB$ and $N$ is the midpoint of $BC.$ The segments $DM$ and $DN$ intersect $AC$ at $P$ and $Q$, respectively. If $AC = 15,$ what is $QA$?
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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10
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logical_31
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Starting from the green dot, find the path to point C. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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Point E.
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logical/31.jpg
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logical/rs_31.jpg
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logical_32
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Starting from the green dot, find the path to point E. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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Point B.
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logical/32.jpg
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logical/rs_32.jpg
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logical_33
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Starting from the green dot, find the path to point D. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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Point C.
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logical/33.jpg
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logical/rs_33.jpg
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logical_34
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Starting from the green dot, find the path to point C. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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Point D, A.
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logical/34.jpg
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logical/rs_34.jpg
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logical_35
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Starting from the green dot, find the path to point E. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
|
Point C.
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logical/35.jpg
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logical/rs_35.jpg
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logical_36
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Starting from the green dot, find the path to point C. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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Point D, A.
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logical/36.jpg
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logical/rs_36.jpg
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logical_37
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Starting from the green dot, find the path to point A. List the points you pass through in order.
Hint: Draw the path on maze to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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Point D, B, C.
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logical/37.jpg
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logical/rs_37.jpg
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logical_38
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Identify the least number of steps needed to move from the green square to the letter at greatest distance, using only valid horizontal/vertical moves around obstacles
Options: (A) 13, (B) 19, (C) 14, (D) 12
Hint: Draw auxiliary lines to solve the problem. First generate an image with the auxiliary lines overlaid on the given figure, then perform your reasoning and provide the final answer.
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logical
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The answer is (A) 13.
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logical/38.jpg
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logical/rs_38.jpg
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perception_1
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First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/1.jpg
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perception/rs_1.jpg
| null |
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perception_2
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/2.jpg
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perception/rs_2.jpg
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perception_3
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/3.jpg
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perception/rs_3.jpg
| null |
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perception_4
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/4.jpg
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perception/rs_4.jpg
| null |
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perception_5
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/5.jpg
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perception/rs_5.jpg
| null |
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perception_6
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/6.jpg
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perception/rs_6.jpg
| null |
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perception_7
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First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/7.jpg
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perception/rs_7.jpg
| null |
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perception_8
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/8.jpg
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perception/rs_8.jpg
| null |
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perception_9
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/9.jpg
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perception/rs_9.jpg
| null |
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perception_10
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/10.jpg
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perception/rs_10.jpg
| null |
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perception_11
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
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perception
| null |
perception/11.jpg
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perception/rs_11.jpg
| null |
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perception_12
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/12.jpg
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perception/rs_12.jpg
| null |
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perception_13
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/13.jpg
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perception/rs_13.jpg
| null |
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perception_14
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/14.jpg
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perception/rs_14.jpg
| null |
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perception_15
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/15.jpg
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perception/rs_15.jpg
| null |
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perception_16
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/16.jpg
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perception/rs_16.jpg
| null |
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perception_17
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/17.jpg
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perception/rs_17.jpg
| null |
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perception_18
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/18.jpg
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perception/rs_18.jpg
| null |
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perception_19
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/19.jpg
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perception/rs_19.jpg
| null |
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perception_20
|
First generate a completed image by filling in the missing top half of the puzzle. Then, compare your generated full image with the original to validate consistency. Finally, choose the option based on your generated full image that correctly completes the jigsaw. Do not answer before generating the completed image. Output: (1) Generated full image, (2) your reasoning after comparison, (3) Final answer.
| Not supported with pagination yet |
perception
| null |
perception/20.jpg
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perception/rs_20.jpg
| null |
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