Rotations

90° ROTATIONS

100

Rotate (3, 2) 90° counterclockwise.

(−2, 3)

200

Rotate (−4, 1) 90° counterclockwise.

(−1, −4)

300

Rotate (5, −2) 90° counterclockwise.

(2, 5)

400

What is the rule for 90° counterclockwise rotation?

(x, y) → (−y, x)

500

Rotate triangle A(1,2), B(3,2), C(2,4) 90° counterclockwise

A′(−2,1), B′(−2,3), C′(−4,2)

180° ROTATIONS

100

Rotate (2, 3) 180° about the origin

(−2, −3)

200

Rotate (−5, 4) 180° about the origin

(5, −4)

300

Rotate (6, −1) 180° about the origin

(−6, 1)

400

What is the rule for 180° rotation about the origin?

(x, y) → (−x, −y)

500

Rotate triangle A(2,1), B(4,3), C(3,5) 180° about the origin

A′(−2,−1), B′(−4,−3), C′(−3,−5)

270° ROTATIONS

100

Rotate (3, 4) 270° counterclockwise.

(4, −3)

200

Rotate (−2, 5) 270° counterclockwise.

(5, 2)

300

Rotate (6, −3) 270° counterclockwise

(−3, −6)

400

What is the rule for 270° counterclockwise rotation?

(x, y) → (y, −x)

500

Rotate triangle A(1,3), B(2,5), C(4,2) 270° counterclockwise rotation

A′(3,−1), B′(5,−2), C′(2,−4)

DIRECTION MATTERS

100

Rotate (2, 3) 90° clockwise.

(3, −2)

200

Rotate (−4, 2) 90° clockwise.

(2, 4)

300

What is the rule for 90° clockwise rotation?

(x, y) → (y, −x)

400

Is 270° counterclockwise the same as 90° clockwise?

Yes

500

Rotate (5, −1) 90° clockwise

(−1, −5)

THINKING & REASONING

100

Does a rotation change the shape or size?

No

200

What point do rotations in this lesson happen around?

The origin (0,0)

300

A point returns to its original position after what rotation?

360°

400

Which rotation gives the same result as reflecting over both axes?

180° rotation

500

True or False: A student says 90° CCW rule is (x, y) → (y, x). If false, correct it

False (−y, x)