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 #4 : Angles And Their Mesures: Ccss.Math.Content.8.G.A.1b

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

13

Possible Answers:

Translation down

 rotation 

A reflection over the x-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 line was not rotated  because that rotation would have caused the vertical, base, line of the angle to go from being horizontal to vertical, but the line is still horizontal. The line was not reflected over the x-axis because the angle was not flipped and the base of the angle is the straight line, like that of the black angle; thus, the correct answer is a translation down.  

Example Question #4 : Geometric Translations

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

15

Possible Answers:

Translation to the left

 rotation 

A reflection over the y-axis

Correct answer:

Translation 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 line was not rotated  because that rotation would have caused direction of the angle to turn a bit, but the angle's direction did not change. The line was not reflected over the y-axis because the angle was not flipped and the opening of the angle is not facing the opposite direction; thus, the correct answer is a translation to the left.  

Example Question #11 : Angles And Their Mesures: Ccss.Math.Content.8.G.A.1b

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

16

Possible Answers:

A  rotation

A reflection over the x-axis 

A translation up and to the right

Correct answer:

A translation up and to the right

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 line was not rotated  because that rotation would have caused direction of the angle to turn a bit, but the angle's direction did not change. The line was not reflected over the y-axis because the angle was not flipped and the opening of the angle is not facing the opposite direction; thus, the correct answer is a translation up and to the right.  

Example Question #12 : Angles And Their Mesures: Ccss.Math.Content.8.G.A.1b

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

14

Possible Answers:

A reflection over the y-axis 

 rotation 

Translation to the right

Correct answer:

Translation to the right

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 line was not rotated  because that rotation would have caused direction of the angle to turn a bit, but the angle's direction did not change. The line was not reflected over the y-axis because the angle was not flipped and the opening of the angle is not facing the opposite direction; thus, the correct answer is a translation up and to the left.  

Example Question #1 : 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. 

1

Possible Answers:

 rotation 

A translation to the left

A reflection over the x-axis

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 black lines rotate  counterclockwise, or left around the y-axis. The lines are facing the opposite direction, which would happen when the lines are rotated; thus the transformation is a rotation. 

2

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

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

Example Question #1 : 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. 

1

Possible Answers:

Reflection over the y-axis

A , clockwise rotation

Translation to the left

Correct answer:

Reflection over the y-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 , clockwise because that rotation would have caused the lines to move to the right, but the lines were moved to the right. The lines were not moved to the left, as the translation is described in the answer choice, because the lines changed direction; thus, the correct answer is a reflection over the y-axis. 

Example Question #24 : 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. 

3

Possible Answers:

Translation to the left

 rotation

Reflection over the x-axis

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 left around the y-axis, and the rotation was . Also, the lines changed from being horizontal to vertical, which is a sign that the lines were rotated; thus the transformation is a rotation. 

4

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

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

Example Question #25 : 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. 

5

Possible Answers:

 rotation

A translation down

A reflection over the x-axis

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 black lines rotates  counterclockwise, or left around the y-axis; thus the transformation is a rotation. 

6

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

The transformation can't be a translation down because the lines didn't not move down.

Example Question #21 : 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. 

5

Possible Answers:

 rotation 

A reflection over the x-axis

Translation to the left

Correct answer:

Translation 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 vertical, but the lines are still horizontal. The lines were not reflected over the x-axis; thus the correct answer is a translation to the left. 

Example Question #3 : 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. 

5

Possible Answers:

Reflection over the y-axis

 rotation

A translation down and to the right 

Correct answer:

Reflection over the y-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 lines to be vertical, but the lines are still horizontal. The line was not moved down and to the right, as the translation is described in the answer choice; thus, the correct answer is a reflection over the y-axis. 

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