Common Core: 8th Grade Math : Parallel Lines: CCSS.Math.Content.8.G.A.1c

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

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Example Questions

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:

A reflection over the x-axis

\displaystyle 90^\circ rotation 

A translation to the left

Correct answer:

\displaystyle 90^\circ 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 \displaystyle 90^\circ 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 #2 : 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:

A \displaystyle 90^\circ, clockwise rotation

Reflection over the y-axis

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 \displaystyle 90^\circ, 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 #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. 

3

Possible Answers:

\displaystyle 90^\circ rotation

Translation to the left

Reflection over the x-axis

Correct answer:

\displaystyle 90^\circ 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 \displaystyle 90^\circ. 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 #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. 

5

Possible Answers:

A translation down

\displaystyle 180^\circ rotation

A reflection over the x-axis

Correct answer:

\displaystyle 180^\circ 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 \displaystyle 1800^\circ 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 #341 : Grade 8

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:

Translation to the left

\displaystyle 90^\circ rotation 

A reflection over the x-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 lines were not rotated \displaystyle 90^\circ 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 #6 : 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:

A translation down and to the right 

Reflection over the y-axis

\displaystyle 90^\circ rotation

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 \displaystyle 90^\circ 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. 

Example Question #7 : 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. 

8

Possible Answers:

A reflection over the y-axis

A translation down

\displaystyle 90^\circ rotation 

Correct answer:

\displaystyle 90^\circ 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 \displaystyle 90^\circ; 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 #2 : 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. 

9

Possible Answers:

\displaystyle 90^\circ 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 \displaystyle 90^\circ 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 #9 : 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. 

9

Possible Answers:

Translation down

Reflection over the y-axis

\displaystyle 90^\circ rotation 

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 \displaystyle 90^\circ 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 #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. 

10

Possible Answers:

\displaystyle 10^\circ 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 \displaystyle 10^\circ because that rotation would have moved the lines to a \displaystyle 10^\circ 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. 

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