# ISEE Lower Level Quantitative : Geometric Translations

## Example Questions

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### 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.

A reflection over the y-axis

rotation

A translation down

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.

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 #8 : 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.

Reflection over the x-axis

A translation to the left

rotation

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 #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.

rotation

Translation down

Reflection over the y-axis

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 #10 : 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.

Reflection over the x-axis

rotation

A translation to the left

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 #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.

Reflection over the y-axis

rotation

Translation down

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 : 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.

A reflection over the y-axis

A translation down and to the left

rotation

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.

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