Year 6 Maths worksheet on rotation of shapes on a coordinate grid.

Explanation:
To solve this problem, we need to rotate each shape twice: first by 90° clockwise, then by 180° clockwise. We do this step by step.

Step 1: Rotate the shape by 90° clockwise around the origin (0,0).
- To rotate a point (x, y) by 90° clockwise, the new coordinates become (y, -x).
- We apply this rule to each corner of the shape.

Step 2: Take the result from Step 1 and rotate it by 180° clockwise.
- To rotate a point (x, y) by 180° clockwise, the new coordinates become (-x, -y).
- Again, apply this to each corner of the shape.

Let’s go through each shape:

1. Shape 1: A right triangle with vertices at (0,0), (3,0), and (0,3).
- Rotate 90° clockwise: (0,0) → (0,0); (3,0) → (0,-3); (0,3) → (3,0).
New points: (0,0), (0,-3), (3,0).
- Rotate 180°: (0,0) → (0,0); (0,-3) → (0,3); (3,0) → (-3,0).
Final points: (0,0), (0,3), (-3,0).
- This is a triangle in the second quadrant.

2. Shape 2: A 2×1 rectangle from (1,0) to (3,0) to (3,1) to (1,1).
- Rotate 90° clockwise: (1,0) → (0,-1); (3,0) → (0,-3); (3,1) → (1,-3); (1,1) → (1,-1).
New points: (0,-1), (0,-3), (1,-3), (1,-1).
- Rotate 180°: (0,-1) → (0,1); (0,-3) → (0,3); (1,-3) → (-1,3); (1,-1) → (-1,1).
Final points: (0,1), (0,3), (-1,3), (-1,1).
- This is a rectangle in the second quadrant.

3. Shape 3: A right triangle with vertices at (0,0), (-3,0), and (0,3).
- Rotate 90° clockwise: (0,0) → (0,0); (-3,0) → (0,3); (0,3) → (3,0).
New points: (0,0), (0,3), (3,0).
- Rotate 180°: (0,0) → (0,0); (0,3) → (0,-3); (3,0) → (-3,0).
Final points: (0,0), (0,-3), (-3,0).
- This is a triangle in the third quadrant.

4. Shape 4: A trapezoid with vertices at (-3,-1), (-3,-3), (1,-3), and (1,-1).
- Rotate 90° clockwise: (-3,-1) → (-1,3); (-3,-3) → (-3,3); (1,-3) → (-3,-1); (1,-1) → (-1,-1).
New points: (-1,3), (-3,3), (-3,-1), (-1,-1).
- Rotate 180°: (-1,3) → (1,-3); (-3,3) → (3,-3); (-3,-1) → (3,1); (-1,-1) → (1,1).
Final points: (1,-3), (3,-3), (3,1), (1,1).
- This shape is now in the first and fourth quadrants.

5. Shape 5: A staircase shape with points at (0,0), (1,0), (1,1), (2,1), (2,2), (3,2), (3,3), (0,3).
- Rotate 90° clockwise: (0,0) → (0,0); (1,0) → (0,-1); (1,1) → (1,-1); (2,1) → (1,-2); (2,2) → (2,-2); (3,2) → (2,-3); (3,3) → (3,-3); (0,3) → (3,0).
New points: (0,0), (0,-1), (1,-1), (1,-2), (2,-2), (2,-3), (3,-3), (3,0).
- Rotate 180°: (0,0) → (0,0); (0,-1) → (0,1); (1,-1) → (-1,1); (1,-2) → (-1,2); (2,-2) → (-2,2); (2,-3) → (-2,3); (3,-3) → (-3,3); (3,0) → (-3,0).
Final points: (0,0), (0,1), (-1,1), (-1,2), (-2,2), (-2,3), (-3,3), (-3,0).
- This is a staircase in the second quadrant.

6. Shape 6: A pentagon with vertices at (1,1), (3,1), (3,3), (2,2), (1,3).
- Rotate 90° clockwise: (1,1) → (1,-1); (3,1) → (1,-3); (3,3) → (3,-3); (2,2) → (2,-2); (1,3) → (3,-1).
New points: (1,-1), (1,-3), (3,-3), (2,-2), (3,-1).
- Rotate 180°: (1,-1) → (-1,1); (1,-3) → (-1,3); (3,-3) → (-3,3); (2,-2) → (-2,2); (3,-1) → (-3,1).
Final points: (-1,1), (-1,3), (-3,3), (-2,2), (-3,1).
- This shape is in the second quadrant.

Final Answer:
The rotated shapes are as described above. Each shape has been rotated 90° clockwise, then 180° clockwise, resulting in the final positions listed for each.