Common Core: 8th Grade Math : Grade 8

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

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Example Questions

Example Question #852 : Geometry

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


13

Possible Answers:

A reflection over the y-axis 

A translation down and to the right 

 rotation 

Correct answer:

A 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 line was not rotated  because that rotation would have caused the line to be vertical, but the line is 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. 

Example Question #1 : Geometry

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


14

Possible Answers:

A reflection over the x-axis

A  rotation 

A translation down and to the left

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 line was not rotated  because that rotation would have caused the line to be vertical, but the line is still horizontal. The line was not reflected over the x-axis because that transformation would have caused the orange line to be in the bottom right quadrant; thus, the correct answer is a translation down and to the left. 

Example Question #3 : Geometry

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


15

Possible Answers:

A translation up and to the left

A reflection over the x-axis 

 rotation 

Correct answer:

A translation up 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 line was not rotated  because that rotation would have caused the line to be vertical, but the line is still horizontal. The line was not reflected over the x-axis because that transformation would have caused the orange line to be in the bottom right quadrant; thus, the correct answer is a translation up and to the left. 

Example Question #4 : Geometry

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


16

Possible Answers:

 rotation 

A translation down and to the right

A reflection over the y-axis 

Correct answer:

A translation down 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 the line to be vertical, but the line is still horizontal. The line was not reflected over the y-axis because that transformation would have caused the orange line to be in the top left quadrant; thus, the correct answer is a translation down and to the right. 

 

Example Question #5 : Geometry

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


17

Possible Answers:

A translation down and to the right

 rotation 

A reflection over the y-axis 

Correct answer:

A translation down 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 the line to be horizontal, but the line is still vertical. The line was not reflected over the y-axis because that transformation would have caused the orange line to be in the top left quadrant; thus, the correct answer is a translation down and to the right. 

Example Question #851 : Geometry

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


12

Possible Answers:

A reflection over the x-axis 

A translation to the left

 rotation 

Correct answer:

A 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 line was 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 #852 : Geometry

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

10

Possible Answers:

 rotation 

A translation down and to the right

A reflection over the y-axis 

Correct answer:

A 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 line was not rotated  because that rotation would have caused the line to be horizontal, but the line is still vertical. 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. 

Example Question #831 : Geometry

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. 

1

Possible Answers:

A reflection over the x-axis 

A translation to the left

 rotation 

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 angle rotates  counterclockwise, or left around the y-axis. The vertical, base, line of the angle goes from being vertical to horizontal; thus the transformation is a rotation. 

2

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

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

Example Question #832 : Geometry

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. 

3

Possible Answers:

 rotation 

A reflection over the x-axis 

A translation to the left

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 angle rotates  counterclockwise, or left around the y-axis. The vertical, base, line of the angle goes from being the base, to the top; thus the transformation is a rotation. 

4

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

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

Example Question #833 : Geometry

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. 

5

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 black angle rotates  clockwise, or right around the x-axis. The vertical, base, line of the angle goes from being vertical to horizontal; thus the transformation is a rotation. 

6

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

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

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