Topics
8. Transformations & Congruence
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United States of America
Grade 8

8.02 Properties of reflections

Lesson
Practice

Introduction

We have learned about  translation  as an example of transformation where there is no change in shape and size. We'll now learn about another type of transformation which also deals only with a change in orientation of shape or object, known as reflection.

Reflections

A reflection is what occurs when we flip an object or shape across a line. Like a mirror, the object is exactly the same size, just flipped in position. So what was on the left may now appear on the right. Every point on the object or shape has a corresponding point on the image, and they will both be the same distance from the reflection line.

Exploration

Have a quick play with this interactive. Here you can change the shape of the object and the position of the mirror line.

Loading interactive...

The vertices of the triangle and its reflection have the same distance from the mirror line. The reflection is the mirror image of the original triangle on the other side of the line.

Examples

Example 1

Which of the following does not show reflection?

A
An image of two identical musical note facing opposite each other.
B
An image of two triangle. Ask your teacher for more information.
C
An image of 2 identical ogres. One is standing straight facing front and the other one is upside down facing front.
D
An image of two identical elephants facing each other.
Worked Solution
Create a strategy

Remember, a reflection is when the object flipped or reflected across a line.

Apply the idea

Which of object has not been flipped?

The correct answer is B.

An image of two triangle. Ask your teacher for more information.
Idea summary

A reflection is when we flip an object or shape across a line. Like a mirror, the object is exactly the same size, just flipped in position. Every point on the object or shape has a corresponding point on the image, and they will both be the same distance from the reflection line.

Reflections across an axis

As we saw above, a reflection occurs when we flip an object or shape across a line like a mirror. We can reflect points, lines, or polygons on a graph by flipping them across an axis or another line in the plane.

Reflecting over the y-axis

A triangle reflected over the y axis. Ask your teacher for more information.

Note how the point (-2,1) becomes (2,1). The y-value has stayed the same while the x-value has changed signs. In this diagram, the image is reflected across y-axis.

Similarly the point (-6,3) becomes (6,3). The y-value have stayed the same and the x-value has changed signs.

Reflecting over the x-axis

A triangle reflected over the x axis. Ask your teacher for more information.

Note how the point (4,3) becomes (4,-3). The x-value has stayed the same while the y-value has changed signs. In this diagram, the image is reflected across y-axis.

Similarly the point (0,5) becomes (0,-5). The x-value have stayed the same and the y-value has changed signs.

If we reflect horizontally across the y-axis, then the y-values of the coordinates remain the same and the x-values change sign.

If we reflect vertically across the x-axis, the x-values of the coordinates will remain the same and the y-values will change sign.

Examples

Example 2

The point A(2, -2) is plotted on the coordinate plane below.

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y

Plot point A', which is a reflection of point A about the x-axis.

Worked Solution
Create a strategy

Change the sign of the y-coordinate to plot the reflection.

Apply the idea

A(2,-2)'s reflection is A'(2,2).

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Example 3

Plot the following.

a

Plot the line segment AB, where the endpoints are A(-6,-1), and B(10,8).

Worked Solution
Create a strategy

Plot and connect the points.

Apply the idea
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x
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y
b

Plot the reflection of the line segment about the y-axis.

Worked Solution
Create a strategy

Change the signs of the x-coordinates to plot the reflection.

Apply the idea

A(-6,-1)'s reflection is A'(6,-1).

B(10,8)'s reflection is B'(-10,8).

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x
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y
Idea summary

If we reflect horizontally across the y-axis, then the y-values of the coordinates remain the same and the x-values change sign.

If we reflect vertically across the x-axis, the x-values of the coordinates will remain the same and the y-values will change sign.

Outcomes

8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations.

8.G.A.1.A

Lines are taken to lines, and line segments to line segments of the same length.

8.G.A.1.B

Angles are taken to angles of the same measure.

8.G.A.1.C

Parallel lines are taken to parallel lines.

8.G.A.3

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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