MA 08 Geometry

6.9 Rotations

04/21/23 6.9 Rotations 2

Goals

Identify rotations in the plane. Apply rotation formulas to figures

on the coordinate plane.

04/21/23 6.9 Rotations 3

Rotation

A transformation in which a figure is turned about a fixed point, called the center of rotation.

Center of Rotation

04/21/23 6.9 Rotations 4

Rotation

Rays drawn from the center of rotation to a point and its image form an angle called the angle of rotation.

Center of Rotation

90

G

G’

04/21/23 6.9 Rotations 5

Rotations on the Coordinate Plane

Know the translation formulas for:

•90 rotations

•180 rotations

•clockwise & counter-clockwise

Unless told otherwise, the center of rotation is the origin (0, 0).

04/21/23 6.9 Rotations 6

90 clockwise rotation

Formula

(x, y) (y, x)A(-2, 4)

A’(4, 2)

04/21/23 6.9 Rotations 7

Rotate (-3, -2) 90 clockwise

Formula

(x, y) (y, x)

(-3, -2)

A’(-2, 3)

04/21/23 6.9 Rotations 8

90 counter-clockwise rotation

Formula

(x, y) (y, x)

A(4, -2)

A’(2, 4)

04/21/23 6.9 Rotations 9

Rotate (-5, 3) 90 counter-clockwise

Formula

(x, y) (y, x)

(-3, -5)

(-5, 3)

04/21/23 6.9 Rotations 10

180 rotation

Formula

(x, y) (x, y)

A(-4, -2)

A’(4, 2)

04/21/23 6.9 Rotations 11

Rotate (3, -4) 180

Formula

(x, y) (x, y)

(3, -4)

(-3, 4)

04/21/23 6.9 Rotations 12

Rotation Example

Draw a coordinate grid and graph:

A(-3, 0)

B(-2, 4)

C(1, -1)

Draw ABC

A(-3, 0)

B(-2, 4)

C(1, -1)

04/21/23 6.9 Rotations 13

Rotation Example

Rotate RST 90 clockwise.

Formula

(x, y) (y, x)A(-3, 0)

B(-2, 4)

C(1, -1)

04/21/23 6.9 Rotations 14

Rotate ABC 90 clockwise.

(x, y) (y, x)

A(-3, 0) A’(0, 3)

B(-2, 4) B’(4, 2)

C(1, -1) C’(-1, -1)A(-3, 0)

B(-2, 4)

C(1, -1)

A’B’

C’

04/21/23 6.9 Rotations 15

Rotate ABC 90 clockwise.

Check by rotating ABC 90.

A(-3, 0)

B(-2, 4)

C(1, -1)

A’B’

C’

04/21/23 6.9 Rotations 16

Rotating segments

A

B

C

D

E

F

G

H

O

04/21/23 6.9 Rotations 17

Rotating AC 90 CW about the origin maps it to _______.

A

B

C

D

E

F

G

H

CE

O

04/21/23 6.9 Rotations 18

Rotating HG 90 CCW about the origin maps it to _______.

A

B

C

D

E

F

G

H

FE

O

04/21/23 6.9 Rotations 19

Rotating AH 180 about the origin maps it to _______.

A

B

C

D

E

F

G

H

ED

O

04/21/23 6.9 Rotations 20

Rotating GF 90 CCW about point G maps it to _______.

A

B

C

D

E

F

G

H

GH

O

04/21/23 6.9 Rotations 21

Rotating ACEG 180 about the origin maps it to _______.

A

B

C

D

E

F

G

H

EGAC

A E

C

G

O

04/21/23 6.9 Rotations 22

Rotating FED 270 CCW about point D maps it to _______.

A

B

C

D

E

F

G

H

BOD

O

04/21/23 6.9 Rotations 23

Practice Practice Practice