What is similar about these objects?

What do we need to pay attention to when objects are rotated?

Course 2

8-10 Transformations

What am I learning today?Rotations

What will I do to show that I learned it?

Determine coordinates and quadrant resulting from a rotation.

A full turn is a 360° rotation.

90°

180°

360°

How do you determine the How do you determine the angle of rotation?angle of rotation?

What are they rotating around?

270°

A quarter turn is a 90° rotation.

A half turn is a 180° rotation.

A three quarter turn is a 270° rotation.

Course 2

8-10 Rotations

QUESTIONWhat do I need to know to

complete a rotation?

To rotate:

Course 2

8-10 Rotations

- the direction – CW or CCW - the degrees – 90o, 180o, 270o

- the center or point of rotation – origin or point inside the object

Course 2

8-10 Rotations

QUESTIONHow do I rotate an object in the coordinate plane?

Course 2

8-10 Rotations

To Rotate 180o around origin:1. Keep your x- and y-values the same..

2. Move to the opposite quadrant. I to III III to I II to IV IV to II.

3. Put the appropriate signs based on the quadrant.

Course 2

8-10 Rotations

Start: A (-4,3) in quadrant II

Rotate 180o clockwise

Finish: In quadrant IV, so x is positive and y is negative.

A’ (4,-3)

Course 2

8-10 Rotations

To Rotate 90o or 270o around origin:1. x- and y-value switch places. x becomes y and y becomes x..

2. Find the quadrant. Move one for 90o or three for 270o. Pay attention to the direction..

3. Put the appropriate signs based on the quadrant.

Course 2

8-10 Rotations

Start: A (-4,3) in quadrant II

Rotate 270o clockwise

Finish: In quadrant III, so x is negative and y is negative.

A’ (-3,-4)

Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 90° counterclockwise about the origin.

Rotations Around the Origin

Course 2

8-10 Rotations

x

y

A

B

C

3

–3

The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).

The coordinates of the image of triangle ABC are A’(0,1), B’(-3,3), C’(0, 5).

Remember: A 90 degree rotation x and y change places, then pay attention to the

characteristics of the quadrants.

C’

B’

A’

Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 180° counterclockwise about the origin.

Rotations Around the Origin

Course 2

8-10 Rotations

x

y

A

B

C

3

–3

C’

B’

A’

The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).

The coordinates of the image of triangle ABC are A’(-1, 0), B’(-3,-3), C’(-5, 0).

Remember: A 180 degree rotation only changes the signs, so pay attention to the

characteristics of the quadrants.

Triangle ABC has vertices A(1, 0), B(3, 3), C(5, 0). Rotate ∆ABC 270° counterclockwise about the origin.

Rotations Around the Origin

Course 2

8-10 Rotations

x

y

A

B

C

3

–3

The pre-image coordinates of triangle ABC are A(1,0), B(3, 3), C(5,0).

The coordinates of the image of triangle ABC are A’(0,-1), B’(3,-3), C’(0,-5).

Remember: A 270 degree rotation x and y change places, then pay attention to the

characteristics of the quadrants.C’

B’

A’

KK II MM

rotation

PracticeUsing these three points: P(6,3); C(-2,- 4); D(-1,0)

Rotate P 270o CCW

Rotate C 90o CW

Rotate D 180o CW

Rotate P 270o CW

Rotate C 180o CCW

Rotate D 90o CW

P’(3, -6)

C’(-4,2)

D’(1,0)

P’(-3,6)

C’(2,4)

D’(1,0)

Practice

P

R

Q

Graph the pre-image, then rotate 90, 180, and 270 degrees counterclockwise

Now Try These

Graph Triangle MNL with vertices M(0,4), N(3,3), and L(0,0). Rotate 90 degrees clockwise.

Graph Triangle ABC with vertices A(-3, -1), B(-3, -2), and C(1, -2). Rotate 90 degrees clockwise.