📚 Topic Summary
A rotation is a transformation that turns a figure about a fixed point, called the center of rotation. When we rotate a point or shape around the origin (0, 0) on a coordinate plane, specific rules apply for 90°, 180°, and 270° rotations. Understanding these rules allows us to predict the new coordinates of the rotated point or shape without needing a protractor. Let's explore these rules with some practice!
The key is remembering how the x and y coordinates change. For example, a 90° counterclockwise rotation swaps the coordinates and negates the new x-coordinate. A 180° rotation negates both coordinates. A 270° counterclockwise rotation swaps the coordinates and negates the new y-coordinate. Mastering these rotations lays a strong foundation for more complex geometric transformations.
🧮 Part A: Vocabulary
Match the term with its definition:
- Rotation
- Origin
- Coordinate Plane
- Transformation
- Image
- ( ) The starting point of a coordinate plane, (0,0).
- ( ) A change in the position, size, or shape of a figure.
- ( ) The figure resulting from a transformation.
- ( ) A plane formed by the intersection of a horizontal number line (x-axis) and a vertical number line (y-axis).
- ( ) A circular movement of a figure around a fixed point.
✍️ Part B: Fill in the Blanks
Complete the following sentences using the words: clockwise, counterclockwise, origin, 90, 180, 270.
When rotating a figure around the ________, the direction of rotation (__________ or __________) is important. A ______° rotation turns a figure a quarter turn. A ______° rotation turns a figure a half turn. A ______° rotation is a three-quarter turn.
🤔 Part C: Critical Thinking
Explain, in your own words, why understanding rotations around the origin is important in real-world applications. Give at least two examples.