Rotations (A) Worksheet | PDF Printable Geometry Worksheet - Free Printable

I'll solve each rotation problem step by step. Since I can't draw on the image directly, I'll describe how to rotate each shape correctly.

## Rotation Rules

90° Clockwise: Each point (x,y) becomes (y,-x)
90° Counterclockwise: Each point (x,y) becomes (-y,x)
180°: Each point (x,y) becomes (-x,-y)

## Solutions:

1) 90° clockwise

- The blue triangle is rotated 90° clockwise around the marked point.
- Each vertex moves: (x,y) → (y,-x)
- The triangle will be positioned with its right angle pointing downward and to the right.

2) 90° clockwise

- The yellow triangle rotates 90° clockwise.
- The base that was horizontal will now be vertical, pointing downward.
- The triangle will be oriented with its tip pointing to the right.

3) 90° clockwise

- The purple triangle rotates 90° clockwise.
- The hypotenuse will now be vertical, and the right angle will face left.

4) 90° counterclockwise

- The green triangle rotates 90° counterclockwise.
- The triangle will move upward and to the left, with its tip pointing up.

5) 90° counterclockwise

- The purple triangle rotates 90° counterclockwise.
- The triangle will rotate so that its base points to the left.

6) 90° counterclockwise

- The blue triangle rotates 90° counterclockwise.
- The triangle will move upward and to the left, with its tip pointing up.

7) 180°

- The yellow V-shape rotates 180°.
- This creates a mirror image across the center point.
- The V will point downward instead of upward.

8) 180°

- The purple quadrilateral rotates 180°.
- Each vertex moves to the opposite side of the center point.
- The shape appears upside down but maintains its orientation.

9) 180°

- The green parallelogram rotates 180°.
- It will appear upside down with the same dimensions.

10) 90° counterclockwise

- The blue trapezoid rotates 90° counterclockwise.
- The longer base will now be vertical on the left side.
- The shape will be oriented with its "top" pointing to the left.

11) 90° clockwise

- The yellow L-shape rotates 90° clockwise.
- The "arm" that was going right will now go down.
- The "corner" will be in the bottom-right position.

12) 90° counterclockwise

- The purple U-shape rotates 90° counterclockwise.
- The open end will now face to the left.
- The shape will be oriented with the "U" opening to the left.

## How to Perform Rotations:
1. Identify the center of rotation (marked with X)
2. For each vertex of the shape:
- Measure the distance from the center
- Rotate the point according to the specified angle
- Plot the new position
3. Connect the rotated vertices to form the new shape

The key is maintaining the distance from the center point while changing the direction based on the rotation angle. Each rotation preserves the size and shape of the original figure.