Students can use the **Spectrum Math Grade 8 Answer Key** **Chapter 5 Lesson 5.3 Rotations, Reflections, and Translations in the Coordinate Plane** as a quick guide to resolve any of their doubts.

## Spectrum Math Grade 8 Chapter 5 Lesson 5.3 Rotations, Reflections, and Translations in the Coordinate Plane Answers Key

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced. One way to view an image and its transformation is to graph it on a coordinate plane.

**Write whether each transformation is a translation, rotation, reflection, or dilation.**

Question 1.

a.

Answer: translation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

b.

Answer: translation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

c.

Answer: reflection

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

Question 2.

a.

Answer: reflection

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

b.

Answer: dilation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

c.

Answer: rotation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

Question 3.

a.

Answer: translation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

b.

Answer: rotation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

c.

Answer: dilation

A transformation is a change of the position or size of an image. In a translation, an image slides in any direction. In a reflection, an image is flipped over a line. In a rotation, an image is turned about a point. In a dilation, an image is enlarged or reduced.

Graphing figures on a coordinate plane helps show how they are transformed. The original figure is called a preimage. The transformed figure is called the image. Read the numbers on the x-axis and y-axis to determine the location of the figure.

This figure has been rotated 180° about one point of the figure. As a result, the preimage and the image share a point. The 4 corners of the preimage are points A, B, C, and D. The four corners of the image are also labeled A’, B’, C, and D’, but note the prime symbol (‘) after each.

The coordinates of the preimage are: A (-5, 5), B (-3, 6) C(-3, 3), D(0, 3).

The coordinates of the image are: A'(5, 1), B'(3, 0), C'(3, 3), D'(0, 3).

**The location of each figure is identified by the coordinates of its corners. The first figure, or preimage, has coordinate points labeled A, B, etc. The transformed figure, or image, has coordinate points labeled A’, B’, etc.**

Question 1.

What are the coordinates of the preimage?

A'(_____), B'(____), C'(_____), D'(_______)

Answer: (-4, -1) , (-1 , -1) , (-1 , -4) , (-2, -4)

the coordinates of the preimage are (-4, -1) , (-1 , -1) , (-1 , -4) , (-2, -4)

Question 2.

What are the coordinates of the image?

A'(_____), B'(____), C'(_____), D'(_______)

Answer: (-4,1), (-1, 1), (-1, 4), (-2, 4)

The coordinates of the image (-4,1), (-1, 1), (-1, 4), (-2, 4)

Question 3.

What transformation was performed on the figure?

Answer: reflection

The transformation that was performed on the figure is reflection.

Question 4.

What are the coordinates of the preimage?

A(_____), B(____), C(_____)

Answer: (-5, 1), (-1, 1), (-1, 4)

The coordinates of the preimage are (-5, 1), (-1, 1), (-1, 4)

Question 5.

What are the coordinates of the image?

A'(_____), B'(____), C'(_____)

Answer: (-2, -2), (2, -2), (2, 1)

The coordinates of the image are (-2, -2), (2, -2), (2, 1)

Question 6.

What transformation was performed on the figure? _____

Answer: translation

the transformation that was performed on the figure was translation

The location of each figure is identified by the coordinates of its corners. The first figure, or preimage, has coordinate points labeled A, B etc. The transformed figure, or image, has coordinate points labeled A’, B’, etc.

Question 1.

What are the coordinates of the preimage?

A(____) B(____), C(____), D(_____)

Answer: (-4, 3), (0, 3), (-2, 1), (-6, 1)

The coordinates of the preimage are (-4, 3), (0, 3), (-2, 1), (-6, 1)

Question 2.

Draw a transformed image with the following coordinates: A'(__-1, 4__), B'(__5,4__), C'(__2, 1__), D'(__-4, 1__)

Answer:

Question 3.

What transformation did you perform? ________

Answer: dilation

The transformation that was performed on the figure was dilation

Question 4.

What are the coordinates of the preimage?

D (_____), U(____), R(_____)

Answer: (2, 3), (5, 1), (1, 0)

The coordinates of the preimage are (2, 3), (5, 1), (1, 0)

Question 5.

Draw a transformed image with the following coordinates:

D'(__4, -1__), U'(__2, -4__), R'(__1, 0__)

Answer:

Question 6.

What transformation did you perform? _________

Answer: rotation

the transformation that was performed on the figure was rotation.

Question 7.

What are the coordinates of the preimage?

A(_____), W (_____), F (_____), P (_____)

Answer: (2, 5), (5, 3), (5, 1), (0, 0)

The coordinates of the preimage are (2, 5), (5, 3), (5, 1), (0, 0)

Question 8.

Draw a transformed image with the following coordinates: A'(__-2, 5__), W'(__0, 0__), P'(__-5, 3__), P'(__-5, 1__)

Answer:

Question 9.

What transformation did you perform? _____

Answer: reflection

the transformation that was performed was reflection.