Page 2: Practice Problems for Counterclockwise Rotations

This page provides a series of practice problems focusing on counterclockwise rotations of various geometric shapes around the origin.

The problems presented on this page include:

1. Rotating a trapezoid JKLM 270° counterclockwise
2. Rotating a triangle XYZ 180°
3. Rotating a rhombus CDEF 270° counterclockwise
4. Rotating a rectangle TUVW 90° counterclockwise
5. Rotating a parallelogram MNOP 180°
6. Rotating a triangle GHI 270° counterclockwise

Example: For the trapezoid JKLM with vertices J(3, 4), K(6, 4), L(8, 1), and M(1, 1) rotated 270° counterclockwise, the solution shows the new coordinates as J'(4, -3), K'(4, -6), L'(1, -8), and M'(1, -1).

Each problem includes the original coordinates of the shape's vertices and the angle of rotation. The solutions provide the new coordinates of the rotated shape, allowing students to check their work and understand how different angles of rotation affect the final position of the shape.

Highlight: These practice problems help reinforce the rotation rules and provide students with hands-on experience in applying the formulas for different angles of rotation.

The variety of shapes used in these examples (trapezoid, triangle, rhombus, rectangle, parallelogram) demonstrates how rotation affects different geometric figures, helping students develop a comprehensive understanding of rotations in mathematics.

Page 3: Advanced Rotation Problems and Clockwise Rotations

This page introduces more complex rotation problems, including clockwise rotations, and provides additional practice for students.

The page begins with a helpful hint for dealing with clockwise rotations:

Highlight: For clockwise rotations, think of the corresponding counterclockwise rotation and apply that rule.

This tip is crucial for understanding how to approach clockwise rotations using the rules learned for counterclockwise rotations.

The practice problems on this page include:

1. Rotating a square ABCD 90° counterclockwise
2. Rotating a rectangle WXYZ 180°
3. Rotating a triangle DEF 270° counterclockwise
4. Rotating a trapezoid RSTU 180°
5. Rotating a triangle LMN 90° clockwise
6. Rotating a rhombus GHIJ 270° clockwise

Example: For the triangle LMN with vertices L(1, 5), M(3, 8), and N(8, 1) rotated 90° clockwise, the solution shows that this is equivalent to a 270° counterclockwise rotation, resulting in new coordinates L'(5, -1), M'(8, -3), and N'(1, -8).

These problems provide students with opportunities to practice both counterclockwise and clockwise rotations, reinforcing their understanding of how different angles of rotation affect the position of shapes on a coordinate plane.

Vocabulary: Clockwise rotation - A rotation that moves in the same direction as the hands of a clock. Vocabulary: Counterclockwise rotation - A rotation that moves in the opposite direction of the hands of a clock.

The inclusion of clockwise rotations in this section helps students understand the relationship between clockwise and counterclockwise rotations, and how to convert between the two when solving rotation problems.

This page effectively concludes the guide by providing more challenging problems that combine all the concepts learned in the previous sections, ensuring that students have a comprehensive understanding of rotations in mathematics.