Draw a Rotation

• Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR.

• Draw a segment from point R to point A.

• Locate point R' so that AR = AR'.

Rotate quadrilateral RSTV 45° counterclockwise about point A.

• Repeat this process for points S, T, and V.

• Connect the four points to form R'S'T'V'.

Draw a Rotation

Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A.

Answer:

A. A

B. B

C. C

D. D

A. 20° clockwise

B. 20° counterclockwise

C. 90° clockwise

D. 90° counterclockwise

For the following diagram, which description best identifies the rotation of triangle ABC around point Q?

Rotations in the Coordinate Plane

Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 115° clockwise about the point G(–4, –2).

First draw ΔDEF and plot point G.

Use a protractor to measure a 115° angle clockwise with as one side.

Use a compass to copy onto Name the segment

Draw

Repeat with points E and F.

Draw a segment from point G to point D.

Rotations in the Coordinate Plane

Answer: ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G.

A. A

B. B

C. C

D. D

Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1).

A. B.

C. D.

Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin?

A (5, –3)

B (–5, –3)

C (–3, 5)

D (3, –5)

Read the Test Item

You are given a graph of hexagon DGJTSR and asked to identify the coordinates of the image of point T after a 90° counterclockwise rotation about the origin.

Solve the Test Item

To find the coordinates of point T after a 90counterclockwise rotation about the origin, multiply the y-coordinate by –1 and then interchange the x- andy-coordinates.

(x, y) → (–y, x) (5, 3) → (–3, 5)

Answer: The answer is C, (–3, 5).

A. A

B. B

C. C

D. D

A. (–5, –4)

B. (–5, 4)

C. (5, 4)

D. (4, –5)

Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin?