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Chapter 9 19 Glencoe Geometry

9-3 Study Guide and Intervention

Rotations

Draw Rotations A rotation is a transformation that moves every point of the preimage through a specified angle, x°,

and direction about a fixed point called the center of rotation. same point. the same distance from the

center of rotation and the measure of the angle of rotation formed by the preimage, center of rotation, and image

points is x. Example: Use a protractor and ruler to draw a 110° rotation of square LMNO about point P.

Step 1 Draw a segment from

vertex L to point P.

Step 2 Draw a 110° angle

using ܮܲ

Step 3 Use a ruler to draw L'

such that PL' = PL.

Step 4 Repeat steps 13

for vertices M, N, and O and draw square

L' M' N' O'.

Exercises

Use a protractor and a ruler to draw the specified rotation of each figure about point K.

1. 75° 2. 45° 3. 135°

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Chapter 9 20 Glencoe Geometry

9-3 Study Guide and Intervention (continued)

Rotations

Draw Rotations In The Coordinate Plane The following rules can be used to rotate a point 90°, 180°, or 270°

counterclockwise about the origin in the coordinate plane.

To rotate Procedure

90° Multiply the y-x- and y-coordinates.

180° Multiply the x- and y-

270° Multiply the x-x-and y-coordinates.

Example: Parallelogram WXYZ has vertices W(2, 4), X(3, 6), Y(5, 2), and Z(0, 0). Graph parallelogram WXYZ and its image after a rotation of 270° about the origin. Multiply the x-coordinate by 1 and then interchange the x-and y-coordinates. (x, y) ĺ ( y, x)

W(2, 4) ĺ W'(4, 2)

X(3, 6) ĺ X'(6, 3)

Y(5, 2) ĺ Y'(2, 5)

Z(0, 0) ĺ Z'(0, 0)

Exercises

Graph each figure and its image after the specified rotation about the origin.

1. trapezoid FGHI has vertices F(7, 7), 2. ᇞLMN has vertices L(1, 1),

G(9, 2), H(3, 2), and I(5, 7); 90° M(0, 4), and N(6, 2); 90°

3. ᇞABC has vertices A(3, 5), B(0, 2), 4. parallelogram PQRS has vertices P(4, 7),

and C(5, 1); 180° Q(6, 6), R(3, 2), and S(1, 1); 270°quotesdbs_dbs8.pdfusesText_14

[PDF] 9-3 Study Guide and Intervention - Rotations

Chapter 9 19 Glencoe Geometry

9-3 Study Guide and Intervention

Rotations

Step 1 Draw a segment from

Step 2 Draw a 110° angle

Step 3 Use a ruler to draw L'

Step 4 Repeat steps 13

L' M' N' O'.

Exercises

1. 75° 2. 45° 3. 135°

Chapter 9 20 Glencoe Geometry

9-3 Study Guide and Intervention (continued)

Rotations

To rotate Procedure

90° Multiply the y-x- and y-coordinates.

180° Multiply the x- and y-

270° Multiply the x-x-and y-coordinates.

W(2, 4) ĺ W'(4, 2)

X(3, 6) ĺ X'(6, 3)

Y(5, 2) ĺ Y'(2, 5)

Z(0, 0) ĺ Z'(0, 0)

Exercises

1. trapezoid FGHI has vertices F(7, 7), 2. ᇞLMN has vertices L(1, 1),

3. ᇞABC has vertices A(3, 5), B(0, 2), 4. parallelogram PQRS has vertices P(4, 7),