9.3 – Perform Reflections

Reflection:

Transformation that uses a line like a mirror to reflect an image

Line of Reflection:

Mirror line in a reflection

A reflection in a line m maps every point P in the plane to a point , such that:

• If P is not on m, then m is the perpendicular bisector of

• If P is on m, then

'.PP

'P

'P P=

P

Reflect point P(5, 7) in the given line.

'P

P(5, 7) becomes'(5, 7)P −

A reflection in the x-axis changes (x, y) into _______(x, –y)

x – axis

P

Reflect point P(5, 7) in the given line.

'P

P(5, 7) becomes'( 5, 7)P −

A reflection in the y-axis changes (x, y) into _______(–x, y)

y – axis

P

Reflect point P(5, 7) in the given line.

'P

P(5, 7) becomes'(7, 5)P

A reflection in the y = x changes (x, y) into _______(y, x)

y = x

Graph the reflection of the polygon in the given line.

x – axis

'C

'A

'B

Graph the reflection of the polygon in the given line.

y – axis

'C

'A

'B

'D

'C

'A

'B

Graph the reflection of the polygon in the given line.

y = x

(–1 , –3)

(–3, –1)

A=

'A =

(2, –4 )

(–4, 2)

B =

'B =

(3, 0)

(0, 3)

C =

'C =

Graph the reflection of the polygon in the given line.

x – axis

'C

'A

'B

'D

Graph the reflection of the polygon in the given line.

x = –1

'C'A

'B

Graph the reflection of the polygon in the given line.

y = 2'C

'A =

'B

'D=

9.4 – Perform Rotations

Rotation: Transformation that turns a figure about a fixed point

Center of Rotation:

The point that the rotation happens around

Angle of Rotation:

Degree the figure is rotated counterclockwise

A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:

'Q

• If Q is not the center of rotation, then and 'QP Q P= 'm QPQ x∠ = °

PQ

'Q

x°

A rotation about a point P through an angle of x° maps every point Q in the plane to a point such that:

'Q

• If Q is the center of rotation, then 'Q Q=

Q 'Q=

1. Match the diagram with the angle of rotation.

B. 90°

1. Match the diagram with the angle of rotation.

A. 30°

1. Match the diagram with the angle of rotation.

C. 150°

State if the rotation is 90°, 180°, or 270° counter-clockwise.

Counter-clockwise degree of rotation: _______180°

State if the rotation is 90°, 180°, or 270° counter-clockwise.

Counter-clockwise degree of rotation: _______90°

State if the rotation is 90°, 180°, or 270° counter-clockwise.

Counter-clockwise degree of rotation: _______270°

6. Find the value of each variable in the rotation.

x = 4

z = 3

y = z + 2y = 3 + 2

y = 5

6. Find the value of each variable in the rotation.

4s = 24

s = 6

r = 2s – 3 r = 2(6) – 3

r = 9

r = 12 – 3

9.3

9.4

593-594

602-605

WS

3-7, 9, 12 (Graph on worksheet)

3-8, 20, 21, 44-46

ROTATION WS

HW Problems

9.3 #7

A'

B'C '