Common Core: 8th Grade Math : Geometry

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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Example Questions

Example Question #31 : Geometry

Observe the location of the black and orange parallel lines on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black lines have undergone in order to reach the position of the orange lines. Select the answer that provides the correct transformation shown in the provided image. 

8

Possible Answers:

A reflection over the y-axis

 rotation 

A translation down

Correct answer:

 rotation 

Explanation:

First, let's define the possible transformations. 

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

In the images from the question, notice that the lines made a rotation to the right around the x-axis, and the rotation was ; thus the transformation is a rotation. 

7

The transformation can't be a reflection over the y-axis because the orange lines didn't flip over the y-axis. 

The transformation can't be a translation because the lines changed direction, which does not happened when you simply move or slide a line or image. 

Example Question #31 : Geometry

Observe the location of the black and orange parallel lines on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black lines have undergone in order to reach the position of the orange lines. Select the answer that provides the correct transformation shown in the provided image. 

9

Possible Answers:

Reflection over the x-axis

 rotation 

A translation to the left

Correct answer:

Reflection over the x-axis

Explanation:

First, let's define the possible transformations. 

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

In the images from the question, the lines were not rotated  because that rotation would have caused the line to be vertical, but the line is still horizontal. The line was not moved to the left, as the translation is described in the answer choice; thus, the correct answer is a reflection over the x-axis. 

Example Question #31 : Geometric Translations

Observe the location of the black and orange parallel lines on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black lines have undergone in order to reach the position of the orange lines. Select the answer that provides the correct transformation shown in the provided image. 

9

Possible Answers:

 rotation 

Translation down

Reflection over the y-axis

Correct answer:

Translation down

Explanation:

First, let's define the possible transformations. 

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

In the images from the question, the lines were not rotated  because that rotation would have caused the lines to be vertical, but the lines are still horizontal. The lines were not reflected over the y-axis because that transformation would have caused the orange lines to be in the top left quadrant; thus, the correct answer is a translation down. 

Example Question #4 : Parallel Lines: Ccss.Math.Content.8.G.A.1c

Observe the location of the black and orange parallel lines on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black lines have undergone in order to reach the position of the orange lines. Select the answer that provides the correct transformation shown in the provided image. 

10

Possible Answers:

 rotation 

Reflection over the x-axis

A translation to the left

Correct answer:

Reflection over the x-axis

Explanation:

First, let's define the possible transformations. 

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

In the images from the question, the lines were not rotated  because that rotation would have moved the lines to a  slant, not straight. The line was not moved to the left, as the translation is described in the answer choice; thus, the correct answer is a reflection over the x-axis. 

Example Question #35 : Geometry

Observe the location of the black and orange parallel lines on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black lines have undergone in order to reach the position of the orange lines. Select the answer that provides the correct transformation shown in the provided image. 

10

Possible Answers:

 rotation

Reflection over the y-axis

Translation down

Correct answer:

Translation down

Explanation:

First, let's define the possible transformations. 

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

In the images from the question, the lines were not rotated  because that rotation would have caused the lines to be horizontal, but the lines are still vertical. The lines were not reflected over the y-axis because that transformation would have caused the orange lines to be in the top left quadrant; thus, the correct answer is a translation down. 

Example Question #32 : Geometric Translations

Observe the location of the black and orange parallel lines on the provided coordinate plane and identify which of the following transformations—rotation, translation, or reflection—the black lines have undergone in order to reach the position of the orange lines. Select the answer that provides the correct transformation shown in the provided image. 

11

Possible Answers:

A translation down and to the left

 rotation 

A reflection over the y-axis 

Correct answer:

A translation down and to the left

Explanation:

First, let's define the possible transformations. 

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

In the images from the question, the lines were not rotated  because that rotation would have caused the lines to be horizontal, but the lines are still vertical. The lines were not reflected over the y-axis because that transformation would have caused the orange lines to be in the top left quadrant; thus, the correct answer is a translation down and to the left. 

Example Question #1 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape? 

1

Possible Answers:

Yes, translation down

Yes, a rotation 

No

Yes, a reflection over the x-axis

Correct answer:

Yes, a reflection over the x-axis

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent. 

Also, let's recall the types of transformations:

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been flipped; thus, the triangle has been reflected over the x-axis. 

The triangle has not undergone a translation, because a translation would have only moved the triangle, not flipped it. Also, the triangle has not been rotated  because that rotation would have caused the triangle to have its top point facing left or right, not up and down. 

Example Question #32 : Geometry

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape? 


2

Possible Answers:

Yes, translation to the left

Yes, rotation 

No

Yes, reflection over the x-axis

Correct answer:

Yes, rotation 

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent. 

Also, let's recall the types of transformations:

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been rotated ; thus, the triangle has been rotated. The point of the triangle moved from pointing up, to pointing to the left. 

The triangle has not undergone a translation, because a translation would have only moved the triangle, not rotated. Also, the triangle has not been reflected over the x-axis because it doesn't flip over the x-axis. 

Example Question #2 : Understand Congruency Of Two Dimensional Figures: Ccss.Math.Content.8.G.A.2

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape? 


1

Possible Answers:

Yes, rotated 

Yes, translation down

No

Yes, reflected over the y-axis

Correct answer:

Yes, rotated 

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent. 

Also, let's recall the types of transformations:

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been rotated  over the x-axis. 

The triangle has not undergone a translation, because a translation would have only moved the triangle, not flipped or rotated it. The red triangle has not been flipped over the y-axis; thus, the triangle has not been reflected over the y-axis. 

 

Example Question #40 : Geometry

Are the two shapes shown in the coordinate plane congruent? If so, what transformation did the red shape undergo from the orange shape? 

3

Possible Answers:

No

Yes,  rotation

Yes, reflection over the y-axis

Yes, translation to the right

Correct answer:

Yes, reflection over the y-axis

Explanation:

In order to solve this problem, we first need to know what "congruent" means. For two shapes to be congruent, they need to be the same shape and the same size. The shape can go through a transformation—rotation, translation, or reflection—but nothing else about the original shape can be changed for two shapes to be congruent. 

Also, let's recall the types of transformations:

Rotation: A rotation means turning an image, shape, line, etc. around a central point.

Translation: A translation means moving or sliding an image, shape, line, etc. over a plane.

Reflection: A reflection mean flipping an image, shape, line, etc. over a central line. 

For this question, we can tell that the triangles are the same size; thus, the triangles are congruent. The red triangle has been flipped; thus, the triangle has been reflected over the y-axis. 

The triangle has not undergone a translation, because a translation described would have only moved the triangle to the right, not to the left. Also, the triangle has not been rotated  because that rotation would have caused the triangle to have its top point facing left or right, not up and down. 

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