1. Holt McDougal Geometry 9-3 Rotations 9-3 Rotations Holt GeometryHolt McDougal Geometry

2. 9-3 Rotations Warm Up 1. The translation image of P(–3, –1) is P’(1, 3). Find the translation image of Q(2, –4). Solve for x. Round to the nearest tenth. 2. cos 30°= 3. sin 30°=

3. Holt McDougal Geometry 9-3 Rotations Remember that a rotation is a transformation that turns a figure around a fixed point, called the center of rotation. A rotation is an isometry (rigid transformation), so the image of a rotated figure is congruent to the pre-image.

4. Holt McDougal Geometry 9-3 Rotations Tell whether each transformation appears to be a rotation. Explain.

5. Holt McDougal Geometry 9-3 Rotations Unless otherwise stated, all rotations in this book are counterclockwise.

6. Holt McDougal Geometry 9-3 Rotations If the angle of a rotation in the coordinate plane is not a multiple of 90°, you can use sine and cosine ratios to find the coordinates of the image.

7. Holt McDougal Geometry 9-3 Rotations Rotate ΔJKL with vertices J(2, 2), K(4, –5), and L(–1, 6) by 180° about the origin.

8. Holt McDougal Geometry 9-3 Rotations A Ferris wheel has a 100 ft radius and takes 60 s to make a complete rotation. A chair starts at (100, 0). After 5 s, what are the coordinates of its location to the nearest tenth?

9. Holt McDougal Geometry 9-3 Rotations The London Eye observation wheel has a radius of 67.5 m and takes 30 minutes to make a complete rotation. Find the coordinates of the observation car after 6 minutes. Round to the nearest tenth.

10. Holt McDougal Geometry 9-3 Rotations Lesson Quiz 1. Tell whether the transformation appears to be a rotation.

11. Holt McDougal Geometry 9-3 Rotations Rotate ∆RST with vertices R(–1, 4), S(2, 1), and T(3, –3) about the origin by the given angle. 2. 90°

12. Holt McDougal Geometry 9-3 Rotations Rotate ∆RST with vertices R(–1, 4), S(2, 1), and T(3, –3) about the origin by the given angle. 3. 180°