### All Common Core: 8th Grade Math Resources

## Example Questions

### 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.

**Possible Answers:**

Rotation

Translation

Reflection over the y-axis

**Correct answer:**

Rotation

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 both lines share a starting point at the coordinate point . This can be defined as the central point, and the line was rotated to the left; thus the transformation is a rotation.

The transformation can't be a reflection over the y-axis because the orange line didn't flip over the y-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 #1 : Lines And Line Segments: Ccss.Math.Content.8.G.A.1a

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.

**Possible Answers:**

A translation

A reflection over the y-axis

A clockwise rotation

**Correct answer:**

A clockwise rotation

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 line rotates clockwise, or right around the x-axis; thus the transformation is a rotation.

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

**Possible Answers:**

A reflection over the y-axis

A rotation

A translation

**Correct answer:**

A rotation

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 line 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 line didn't flip over the y-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 : Geometry

**Possible Answers:**

A translation

A rotation

A reflection over the y-axis

**Correct answer:**

A rotation

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 both lines share a starting point at the coordinate point . This can be defined as the central point, and the line was rotated to the left; thus the transformation is a rotation.

### Example Question #5 : Geometry

**Possible Answers:**

A rotation

A reflection over the x-axis

A translation to the left

**Correct answer:**

A reflection over the x-axis

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 not have moved the line as far as the orange line was moved. That line would also be slanted at , 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 #6 : Geometry

**Possible Answers:**

A translation down and to the right

A reflection over the y-axis

A rotation

**Correct answer:**

A reflection over the y-axis

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 #7 : Geometry

**Possible Answers:**

A translation down and to the left

A rotation

A reflection over the x-axis

**Correct answer:**

A translation down and to the left

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 #8 : Geometry

**Possible Answers:**

A reflection over the x-axis

A rotation

A translation up and to the left

**Correct answer:**

A translation up and to the left

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 #1 : Lines And Line Segments: Ccss.Math.Content.8.G.A.1a

**Possible Answers:**

A rotation

A translation down and to the right

A reflection over the y-axis

**Correct answer:**

A translation down and to the right

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 #2 : Lines And Line Segments: Ccss.Math.Content.8.G.A.1a

**Possible Answers:**

A reflection over the y-axis

A rotation

A translation down and to the right

**Correct answer:**

A translation down and to the right

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.