Rotation Worksheets - 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 perform each rotation and what the result should look like.

Rotation Rules:
- 90° clockwise: (x,y) → (y,-x)
- 90° anti-clockwise: (x,y) → (-y,x)
- 180°: (x,y) → (-x,-y)

Let me go through each one:

1) 90° clockwise
- The blue triangle is rotated 90° clockwise around the marked point
- Each vertex moves down and to the right relative to the center
- The new position will have the same shape but oriented differently

2) 90° clockwise
- The yellow triangle rotates 90° clockwise around the marked point
- The base will now be horizontal pointing to the right

3) 90° clockwise
- The purple triangle rotates 90° clockwise
- The right angle will now be at the bottom left of the rotation point

4) 90° anti-clockwise
- The green triangle rotates 90° anti-clockwise
- The orientation changes so it points upward instead of to the right

5) 90° anti-clockwise
- The pink triangle rotates 90° anti-clockwise
- The base will now be horizontal pointing to the left

6) 90° anti-clockwise
- The blue triangle rotates 90° anti-clockwise
- It will now point downward instead of to the right

7) 180°
- The yellow V-shape rotates 180°
- It will be upside down and mirrored across the center point

8) 180°
- The purple diamond rotates 180°
- It will be flipped completely, with corners in opposite positions

9) 180°
- The green parallelogram rotates 180°
- It will be flipped horizontally and vertically

10) 90° anti-clockwise
- The blue pentagon rotates 90° anti-clockwise
- The shape will now point to the left instead of down

11) 90° clockwise
- The orange L-shape rotates 90° clockwise
- The "L" will now point to the right instead of up

12) 90° anti-clockwise
- The purple U-shape rotates 90° anti-clockwise
- The "U" will now point to the left instead of up

How to solve these:
1. Identify the center of rotation (marked with X)
2. For each vertex of the shape, measure its distance from the center
3. Apply the appropriate rotation rule:
- 90° clockwise: move the point so it's the same distance but rotated 90° clockwise
- 90° anti-clockwise: move the point so it's the same distance but rotated 90° counter-clockwise
- 180°: move the point to the opposite side of the center, same distance away
4. Connect the new vertices to form the rotated shape

The key is that rotation preserves the size and shape of the figure, only changing its orientation. The distance from each vertex to the center of rotation remains constant.