Rotation practice worksheet for geometry transformations, featuring 12 problems with shapes to rotate on a grid.

To solve these rotation problems, we need to move each shape around the red "X" point (the center of rotation) by the specific angle and direction given.

Here is the step-by-step logic for how to rotate shapes on a grid:
1. Identify Key Points: Pick the corners (vertices) of the shape.
2. Count Squares: Count how many squares right/left and up/down each corner is from the red X.
3. Rotate the Counts:
* 90° Clockwise: Swap the horizontal and vertical distances. If a point was $X$ right and $Y$ up, it becomes $X$ down and $Y$ right. (Think: Right $\rightarrow$ Down, Up $\rightarrow$ Right).
* 90° Anti-clockwise: Swap distances. If a point was $X$ right and $Y$ up, it becomes $X$ up and $Y$ left. (Think: Right $\rightarrow$ Up, Up $\rightarrow$ Left).
* 180°: Keep the same distances but go in the exact opposite direction. If a point was Right and Up, it goes Left and Down.

Let's apply this to each problem:

1) Blue Triangle: 90° Clockwise
* The triangle has a vertical side of length 2 going Up from the X. Rotated 90° clockwise, "Up" becomes Right. So, draw a line 2 squares to the Right.
* The top corner is 3 squares Left and 2 squares Up from the X. Rotated 90° clockwise: Left becomes Down, Up becomes Right. So the new point is 3 squares Down and 2 squares Right from the X.
* Connect these points to form the new triangle.

2) Yellow Triangle: 90° Clockwise
* The top-right corner is 2 squares Left and 1 square Up from the X. Rotated 90° clockwise: Left $\rightarrow$ Down, Up $\rightarrow$ Right. New position: 2 squares Down, 1 square Right.
* The bottom tip is 2 squares Left and 3 squares Down from the X. Rotated 90° clockwise: Left $\rightarrow$ Down, Down $\rightarrow$ Left. New position: 2 squares Down, 3 squares Left.
* Draw the triangle connecting these new points.

3) Purple Triangle: 90° Clockwise
* The vertical side is 2 squares Down from the X. Rotated 90° clockwise: Down $\rightarrow$ Left. New side is 2 squares Left.
* The other corner is 2 squares Left and 2 squares Down from the X. Rotated 90° clockwise: Left $\rightarrow$ Down, Down $\rightarrow$ Left. New position: 2 squares Down, 2 squares Left.
* Draw the triangle.

4) Green Triangle: 90° Anti-clockwise
* The triangle points Right. The tip is 2 squares Right of the X. Rotated 90° anti-clockwise: Right $\rightarrow$ Up. New tip is 2 squares Up.
* The base is vertical, 2 squares long, located 2 squares Right of the X. The top of the base is 2 Right, 1 Up. Rotated anti-clockwise: Right $\rightarrow$ Up, Up $\rightarrow$ Left. New pos: 2 Up, 1 Left. The bottom of the base is 2 Right, 1 Down. Rotated: Right $\rightarrow$ Up, Down $\rightarrow$ Right. New pos: 2 Up, 1 Right.
* The new triangle points Up.

5) Pink Triangle: 90° Anti-clockwise
* Top-left corner is 1 square Left of the X. Rotated anti-clockwise: Left $\rightarrow$ Down. New pos: 1 square Down.
* Top-right corner is 2 squares Right of the X. Rotated anti-clockwise: Right $\rightarrow$ Up. New pos: 2 squares Up.
* Bottom tip is 1 square Right and 2 squares Down from the X. Rotated anti-clockwise: Right $\rightarrow$ Up, Down $\rightarrow$ Right. New pos: 1 square Up, 2 squares Right.
* Connect these points.

6) Blue Triangle: 90° Anti-clockwise
* Vertical side is 3 squares Up from the X. Rotated anti-clockwise: Up $\rightarrow$ Left. New side is 3 squares Left.
* Other corner is 2 squares Right and 3 squares Up from the X. Rotated anti-clockwise: Right $\rightarrow$ Up, Up $\rightarrow$ Left. New pos: 2 squares Up, 3 squares Left.
* Draw the triangle.

7) Yellow Arrowhead: 180°
* 180° means flipping it completely upside down through the center point.
* The top-left tip is 2 squares Left and 2 squares Up. Opposite is 2 squares Right and 2 squares Down.
* The top-right tip is 2 squares Right and 2 squares Up. Opposite is 2 squares Left and 2 squares Down.
* The inner "V" point is 1 square Up. Opposite is 1 square Down.
* The shape will now point downwards.

8) Purple Kite: 180°
* Flip every point to the opposite side of the X.
* Left tip (2 Left) $\rightarrow$ 2 Right.
* Right tip (2 Right, 1 Down) $\rightarrow$ 2 Left, 1 Up.
* Bottom tip (1 Right, 3 Down) $\rightarrow$ 1 Left, 3 Up.
* Draw the kite in this new inverted position.

9) Teal Parallelogram: 180°
* Flip every point to the opposite side.
* Top-left corner (at X) stays at X? No, the X is at the top vertex. Let's trace relative to X.
* The shape extends 1 Right and 3 Down.
* Opposite direction: 1 Left and 3 Up.
* The other corner is 1 Left and 2 Down from X. Opposite: 1 Right and 2 Up.
* The shape moves to the top-left quadrant relative to the X.

10) Blue Trapezoid: 90° Anti-clockwise
* This shape is mostly below and to the right of the X.
* Bottom-left corner is at the X.
* Top-left corner is 4 squares Up. Rotated anti-clockwise: Up $\rightarrow$ Left. New segment goes 4 squares Left from X.
* Top-right corner is 2 squares Right and 4 squares Up. Rotated anti-clockwise: Right $\rightarrow$ Up, Up $\rightarrow$ Left. New pos: 2 squares Up, 4 squares Left.
* Bottom-right corner is 2 squares Right and 1 square Down. Rotated anti-clockwise: Right $\rightarrow$ Up, Down $\rightarrow$ Right. New pos: 2 squares Up, 1 square Right.
* Connect these points.

11) Orange L-Shape: 90° Clockwise
* The corner of the L is 1 square Left and 1 square Up from the X.
* Let's use the inner corner near the X. The vertical part goes 2 squares Down from the level of the horizontal bar. The horizontal bar goes 2 squares Right.
* Let's pick specific vertices relative to X:
* Vertex A (top left of L): 1 Left, 1 Up. Rotate 90° CW: 1 Down, 1 Right.
* Vertex B (inner corner): 1 Right, 1 Down. Rotate 90° CW: 1 Down, 1 Left.
* Vertex C (bottom end): 1 Right, 3 Down. Rotate 90° CW: 3 Left, 1 Down.
* Vertex D (right end): 3 Right, 1 Down. Rotate 90° CW: 1 Left, 3 Down.
* Draw the L-shape connecting these new coordinates. It will look like an L rotated so the long part points Left and the short part points Down.

12) Purple U-Shape: 90° Anti-clockwise
* The shape is to the right and below the X.
* Top-left corner of the U is at the X? No, the X is above the gap.
* Let's trace from X:
* Left-top corner of the shape: 1 Left, 2 Down. Rotate 90° ACW: Left $\rightarrow$ Down, Down $\rightarrow$ Right. New pos: 1 Down, 2 Right.
* Right-top corner of the shape: 3 Right, 2 Down. Rotate 90° ACW: Right $\rightarrow$ Up, Down $\rightarrow$ Right. New pos: 3 Up, 2 Right.
* Bottom-right corner: 3 Right, 4 Down. Rotate 90° ACW: 3 Up, 4 Right.
* Bottom-inner-right: 2 Right, 3 Down. Rotate 90° ACW: 2 Up, 3 Right.
* Bottom-inner-left: 1 Right, 3 Down. Rotate 90° ACW: 1 Up, 3 Right.
* Bottom-left corner: 1 Left, 4 Down. Rotate 90° ACW: 1 Down, 4 Right.
* Essentially, the U-shape which was "opening up" will now be "opening left".

Final Answer:
Since I cannot draw directly on your paper, here are the descriptions of where the new shapes should be drawn relative to the red X for each question:

1. Triangle pointing Right. The vertical side is now horizontal, extending 2 squares to the Right of the X. The third vertex is 2 squares Right and 3 squares Down from the X.
2. Triangle pointing Down-Left. The vertices are at (1 Right, 2 Down), (3 Left, 2 Down), and (1 Left, 0) relative to the original orientation shifted. Specifically: One vertex is 1 square Right and 2 squares Down from X. Another is 3 squares Left and 2 squares Down from X. The third is 1 square Left of the X.
3. Triangle pointing Left. The vertical side is now horizontal, extending 2 squares to the Left of the X. The third vertex is 2 squares Left and 2 squares Down from the X.
4. Triangle pointing Up. The tip is 2 squares Up from the X. The base is horizontal, 2 squares wide, sitting 2 squares above the X.
5. Triangle pointing Up-Right. Vertices are: 1 square Down from X; 2 squares Up from X; and 2 squares Right, 1 square Up from X.
6. Triangle pointing Up-Left. The vertical side is now horizontal, extending 3 squares to the Left of the X. The third vertex is 3 squares Left and 2 squares Up from the X.
7. Arrowhead pointing Down. The tips are 2 squares Right/2 squares Down and 2 squares Left/2 squares Down from the X. The inner point is 1 square Down from the X.
8. Kite inverted. The left tip is 2 squares Right of X. The right tip is 2 squares Left, 1 square Up of X. The bottom tip is 1 square Left, 3 squares Up of X.
9. Parallelogram shifted Top-Left. The shape occupies the space 1 to 2 squares Left and 1 to 3 squares Up from the X.
10. Trapezoid rotated Left. The long vertical side is now horizontal, extending 4 squares to the Left of the X. The shape sits generally in the top-left and bottom-left quadrants relative to the start, but specifically: Top edge goes 4 Left from X. Right side connects (4 Left, 2 Up) to (1 Right, 2 Up). Bottom side connects (1 Right, 2 Up) to X? No, re-verify #10.
* Correction for #10: Original: Vertical side 4 Up from X. Horizontal top 2 Right. Slanted side down to (2 Right, 1 Down).
* Rotated 90° ACW: Vertical side becomes 4 Left from X. Horizontal top becomes 2 Up from the end of that line (so 4 Left, 2 Up). The slanted side goes from (4 Left, 2 Up) to (1 Right, 2 Up)? No.
* Let's stick to vertices for #10:
* V1 (at X): Stays at X.
* V2 (Top Left): 4 Up from X $\rightarrow$ 4 Left from X.
* V3 (Top Right): 2 Right, 4 Up from X $\rightarrow$ 2 Up, 4 Left from X.
* V4 (Bottom Right): 2 Right, 1 Down from X $\rightarrow$ 2 Up, 1 Right from X.
* Draw lines connecting: X $\rightarrow$ (4 Left) $\rightarrow$ (4 Left, 2 Up) $\rightarrow$ (1 Right, 2 Up) $\rightarrow$ X.
11. L-Shape rotated. The long part (originally vertical down) is now horizontal Left. The short part (originally horizontal right) is now vertical Down. The inner corner is 1 square Left and 1 square Down from the X. The shape extends 2 squares Left from there and 2 squares Down from there.
12. U-Shape rotated. The U originally opened Up. Rotated 90° Anti-clockwise, it opens to the Left. The flat bottom of the U is now vertical on the Right. The two prongs point to the Left.