Holt Geometry 12-1 Reflections Introduction and Review Information.

Holt Geometry

12-1 Reflections

Introduction and Review Information

Holt Geometry

12-1 Reflections

Example

A

B

C

Pre-Image

B'

A'

C'

Image

Holt Geometry

12-1 ReflectionsWriting Equations

Remember equations for horizontal lines:

y = 2 is horizontal line crossing y-axis at 2y = –4 is horizontal line crossing y-axis at 4

y=2

y =–4

Holt Geometry

12-1 ReflectionsWriting Equations

Remember equations for vertical lines:

x = 2 is vertical line crossing x-axis at 2x = –4 is vertical line crossing x-axis at –4

x=2x =–4

Holt Geometry

12-1 Reflections12-1 Reflections

Holt Geometry

I CANI CAN

- Accurately reflect a figure in space.- Accurately reflect a figure in space.

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

the line y = x, or the line y = –x the line y = x, or the line y = –x

Holt Geometry

12-1 Reflections

Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line.

Holt Geometry

12-1 Reflections

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.

Holt Geometry

12-1 Reflections

Holt Geometry

12-1 ReflectionsReflecting across vertical lines (x = a)

Reflect across x = 2Step 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'

Holt Geometry

12-1 Reflections

Reflecting across y-axis

C

A T

Pre-image Image

A(-3, 2)

C(-3, 7)

T(2, 2)

C'(3, 7)

A'(3, 2)

T'(-2, 2)

What do you notice aboutthe x and y coordinatesof the pre-image and imagepoints?

C ’

A ’T ’

Holt Geometry

12-1 Reflections

Reflecting across x-axis

Reflect the following shape across the x-axis

A M

T

Pre-image ImageM(2, 1)

A(-1, 1)

T(-3, 5)

What do you notice aboutthe x and y coordinatesof the pre-image and imagepoints?

H(4, 5)

M ’(2, -1)A ’(-1, -1)

T ’(-3, -5)

H ’(4, -5)

H

A ’ M ’

T ’ H ’

Holt Geometry

12-1 Reflections

Reflecting across the line y = x

F I

H S

Pre-Image Image

I(4, 0)

F(-3, 0)

S(4, -9)

H(-3, -9)

I'(0, 4)

F ‘(0, -3)

S'(-9, 4)

H'(-9, -3)

What do you notice aboutthe x and y coordinatesof the pre-image and imagepoints?

F ’

I ’

H ’

S ’

Holt Geometry

12-1 Reflections

Holt Geometry

12-1 Reflections

8. Reflect across y = –x

E V

M O M ’(-2, 5) O’(-2, 2)

V ’(-6, 0) E’(-6, -7)

M(-5, 2) O(-2, 2)

V(0, 6) E(-7, 6)M ’

O ’V ’

E ’

Holt Geometry

12-1 Reflections

8. Reflect across y = -3

H ’(-12, 2)

A ’(7, -7)

T ’(2, -7)

H

T A

Holt Geometry

12-1 Reflections

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 ’