A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called a

mapping.

Examples of transformations are: translations, reflections, rotations, and dilations.

Preimage:the original figure

Image:the figure after the

transformation

Isometry: a transformation that does not

change the size or shape of a figure

Which of the transformations are examples of isometry?

Translations, reflections, and rotations

12-1 Reflections

Holt Geometry

I CAN

- Accurately reflect a figure in space.

- Reflect a figure across the x-axis, the y-axis

the line y = x, or the line y = –x

Reflection:

Reflection is a transformation that moves a figure by flipping it across a line

Reflection

The original figure is called the preimage and the reflected figure is called the image.

A reflection is the reflected image always congruent to the preimage?

What do we call this?

Example 1: Identifying Reflections

Tell whether each transformation appears to be a reflection. Explain.

No; the image does notAppear to be flipped.

Yes; the image appears to be flipped across a line.

A. B.

Check It Out! Example 1

Tell whether each transformation appears to be a reflection.

a. b.

No; the figure does not appear to be flipped.

Yes; the image appears to be flipped across a line.

We are going to reflect images on the coordinate plane across given lines

Reflecting across vertical lines (x = a)

Reflect across x = -2

Step 1 – Draw line of reflection

A B

CD

Step 2 – Pick a starting point, count over-ALWAYS vertically or horizontally to line

Step 3 – Go that same distance on the other side of line

Step 4 – LABEL THE NEW POINTS

Step 5 – Continue with other points

B'

C'

A'

D'

Do # 3 on your worksheetLabel the coordinates of the preimage.

Reflecting across y-axis

Reflect the following shape across the y-axis

Pre-image Image

B( , )

A( , )

C( , )

A'( , )

B'( , )

C'( , )

Do # 4 on your worksheetLabel the coordinates of the preimage.

A

B

C

Reflecting across x-axis

Reflect the following shape across the x-axis

A

B C

Pre-image Image

B( , )

A( , )

C( , )

A'( , )

B'( , )

C'( , )

Do #5 on your worksheetLabel the coordinates of the preimage.

Reflecting across the line y = x

F I

H S

Pre-Image Image

I( , )

F( , )

S( , )

H( , )

I'( , )

F'( , )

S'( , )

H'( , )

Do #6 on your worksheetLabel the coordinates of the preimage.

Remember: Move ONLY vertically or horizontally…think about why?

Look back at the problems you just completed.

Compare the x and y-coordinates for the pre-image and image.

Can you see a rule for each reflection?

Check It Out!

Reflect the rectangle with vertices S(3, 4), T(3, 1), U(–2, 1) and V(–2, 4) across the x-axis.

The reflection of (x, y) is (x,–y).

S(3, 4) S’(3, –4)

T(3, 1) T’(3, –1)

U(–2, 1) U’(–2, –1)

V(–2, 4) V’(–2, –4)

Graph the image and preimage.

V S

U T

V’ S’

U’ T’

Reflect across y = –x

A K

C E

C’( , ) A’( , )

K’( , ) E’( , )

Do #8 on your worksheet

Lesson QuizReflect the figure with the given vertices across the given line.

1. A(2, 3), B(–1, 5), C(4,–1); y = xA’(3, 2), B’(5,–1), C’(–1, 4)

2. U(–8, 2), V(–3, –1), W(3, 3); y-axis U’(8, 2), V’(3, –1), W’(–3, 3)

3. E(–3, –2), F(6, –4), G(–2, 1); x-axis E’(–3, 2), F’(6, 4), G’(–2, –1)