Rotation (A) Worksheet | Fun and Engaging PDF Worksheets - Free Printable

To solve these rotation problems, we need to move each shape around the red "X" point. The "X" is the center of rotation, so it stays in the same place while the rest of the shape moves.

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 that are easiest to track. Usually, these are the points furthest from the center "X".
2. Count the Squares: Count how many squares right/left and up/down a key point is from the "X".
3. Apply the Rotation Rule:
* 90° Clockwise: Swap the horizontal and vertical distances. If a point was *Right* and *Up*, it becomes *Down* and *Right*. (Think: Top goes to Right, Right goes to Bottom).
* 90° Anti-clockwise: Swap the distances. If a point was *Right* and *Up*, it becomes *Left* and *Up*. (Think: Top goes to Left, Left goes to Bottom).
* 180°: Keep the distances the same but flip the direction completely. If a point is *Right* and *Up*, it moves to *Left* and *Down*. It looks like the shape has been turned upside down.

Let's apply this to each problem:

1) Blue Triangle: 90° Clockwise
* The top-left corner is 4 squares Left and 3 squares Up from the X.
* Rotate 90° Clockwise: "Left and Up" becomes "Up and Right".
* New Position: 4 squares Up and 3 squares Right from the X.
* The resulting triangle will point to the right.

2) Yellow Triangle: 90° Clockwise
* The bottom tip is 3 squares Down and 2 squares Left from the X.
* Rotate 90° Clockwise: "Down and Left" becomes "Left and Up".
* New Position: 3 squares Left and 2 squares Up from the X.
* The resulting triangle will point upwards.

3) Purple Triangle: 90° Clockwise
* The left corner is 3 squares Left and 2 squares Up from the X.
* Rotate 90° Clockwise: "Left and Up" becomes "Up and Right".
* New Position: 3 squares Up and 2 squares Right from the X.
* The resulting triangle will point to the right.

4) Green Triangle: 90° Anti-clockwise
* The right tip is 3 squares Right from the X.
* Rotate 90° Anti-clockwise: "Right" becomes "Up".
* New Position: 3 squares Up from the X.
* The resulting triangle will point upwards.

5) Pink Triangle: 90° Anti-clockwise
* The right corner is 3 squares Right and 1 square Down from the X.
* Rotate 90° Anti-clockwise: "Right and Down" becomes "Down and Left".
* New Position: 3 squares Down and 1 square Left from the X.
* The resulting triangle will point downwards.

6) Blue Triangle: 90° Anti-clockwise
* The top tip is 4 squares Up and 1 square Right from the X.
* Rotate 90° Anti-clockwise: "Up and Right" becomes "Left and Up".
* New Position: 4 squares Left and 1 square Up from the X.
* The resulting triangle will point to the left.

7) Lime Green Arrowhead: 180°
* This is a half-turn. Every point flips to the opposite side.
* The left wing tip is 3 squares Left and 3 squares Up. It moves to 3 squares Right and 3 squares Down.
* The right wing tip is 3 squares Right and 3 squares Up. It moves to 3 squares Left and 3 squares Down.
* The shape ends up pointing downwards.

8) Purple Kite: 180°
* Flip every point through the center.
* The rightmost point (4 squares Right, 1 square Down) moves to 4 squares Left, 1 square Up.
* The bottom point (2 squares Right, 3 squares Down) moves to 2 squares Left, 3 squares Up.
* The shape looks like the original kite turned upside down.

9) Teal Parallelogram: 180°
* Flip every point through the center.
* The top-right corner (1 square Right, 2 squares Up) moves to 1 square Left, 2 squares Down.
* The bottom-left corner (1 square Left, 3 squares Down) moves to 1 square Right, 3 squares Up.
* The shape is inverted.

10) Blue Trapezoid: 90° Anti-clockwise
* The bottom-right corner is 2 squares Right and 1 square Down.
* Rotate 90° Anti-clockwise: "Right and Down" becomes "Down and Left".
* New Position: 2 squares Down and 1 square Left.
* The whole shape rotates so the long vertical side becomes a horizontal side at the bottom.

11) Orange L-Shape: 90° Clockwise
* The top-left corner of the L is 1 square Left and 1 square Up.
* Rotate 90° Clockwise: "Left and Up" becomes "Up and Right".
* New Position: 1 square Up and 1 square Right.
* The L-shape will look like it is lying on its back, with the long part horizontal at the top.

12) Purple U-Shape: 90° Anti-clockwise
* The bottom-right corner is 3 squares Right and 2 squares Down.
* Rotate 90° Anti-clockwise: "Right and Down" becomes "Down and Left".
* New Position: 3 squares Down and 2 squares Left.
* The U-shape rotates so the opening faces to the left.

Final Answer:
The solutions involve drawing the new positions of the shapes on the grids as described below:

1. Triangle points Right. (Top vertex moves to 4 Up, 3 Right from X).
2. Triangle points Up. (Bottom vertex moves to 3 Left, 2 Up from X).
3. Triangle points Right. (Left vertex moves to 3 Up, 2 Right from X).
4. Triangle points Up. (Right vertex moves to 3 Up from X).
5. Triangle points Down. (Right vertex moves to 3 Down, 1 Left from X).
6. Triangle points Left. (Top vertex moves to 4 Left, 1 Up from X).
7. Arrowhead points Down. (Symmetrical inversion through X).
8. Kite is Upside Down. (Inverted through X).
9. Parallelogram is Inverted. (Inverted through X).
10. Trapezoid lies on its base. (Rotated so the vertical side becomes horizontal at the bottom).
11. L-Shape lies on its back. (Long side is horizontal at the top, short leg points down on the right).
12. U-Shape opens to the Left. (Rotated so the opening faces left).