Geometry Worksheets | Transformations Worksheets - Free Printable

I'll solve each rotation problem step by step, finding the coordinates of the rotated shapes.

Problem 1: Rotation 180° about the origin
Original shape vertices appear to be at: (0,0), (2,0), (2,1)
For 180° rotation: (x,y) → (-x,-y)
- (0,0) → (0,0)
- (2,0) → (-2,0)
- (2,1) → (-2,-1)

Rotated vertices: (0,0), (-2,0), (-2,-1)

Problem 2: Rotation 180° about the origin
Original shape vertices appear to be at: (2,3), (4,3), (4,5), (2,5)
For 180° rotation: (x,y) → (-x,-y)
- (2,3) → (-2,-3)
- (4,3) → (-4,-3)
- (4,5) → (-4,-5)
- (2,5) → (-2,-5)

Rotated vertices: (-2,-3), (-4,-3), (-4,-5), (-2,-5)

Problem 3: Rotation 90° counterclockwise about the origin
Original shape vertices appear to be at: (2,4), (4,4), (4,2)
For 90° CCW rotation: (x,y) → (-y,x)
- (2,4) → (-4,2)
- (4,4) → (-4,4)
- (4,2) → (-2,4)

Rotated vertices: (-4,2), (-4,4), (-2,4)

Problem 4: Rotation 180° about the origin
Original shape appears to be a rectangle with vertices at: (1,1), (3,1), (3,3), (1,3)
For 180° rotation: (x,y) → (-x,-y)
- (1,1) → (-1,-1)
- (3,1) → (-3,-1)
- (3,3) → (-3,-3)
- (1,3) → (-1,-3)

Rotated vertices: (-1,-1), (-3,-1), (-3,-3), (-1,-3)

Problem 5: Rotation 90° clockwise about the origin
Original shape is an L-shape with vertices approximately at: (-3,-2), (-3,-1), (-2,-1), (-2,1), (-1,1), (-1,-2)
For 90° CW rotation: (x,y) → (y,-x)
- (-3,-2) → (-2,3)
- (-3,-1) → (-1,3)
- (-2,-1) → (-1,2)
- (-2,1) → (1,2)
- (-1,1) → (1,1)
- (-1,-2) → (-2,1)

Rotated vertices: (-2,3), (-1,3), (-1,2), (1,2), (1,1), (-2,1)

Problem 6: Rotation 90° counterclockwise about the origin
Original shape is an L-shape with vertices approximately at: (2,2), (2,4), (3,4), (3,3), (4,3), (4,2)
For 90° CCW rotation: (x,y) → (-y,x)
- (2,2) → (-2,2)
- (2,4) → (-4,2)
- (3,4) → (-4,3)
- (3,3) → (-3,3)
- (4,3) → (-3,4)
- (4,2) → (-2,4)

Rotated vertices: (-2,2), (-4,2), (-4,3), (-3,3), (-3,4), (-2,4)

Final Answer:
1) Vertices after 180° rotation: (0,0), (-2,0), (-2,-1)
2) Vertices after 180° rotation: (-2,-3), (-4,-3), (-4,-5), (-2,-5)
3) Vertices after 90° CCW rotation: (-4,2), (-4,4), (-2,4)
4) Vertices after 180° rotation: (-1,-1), (-3,-1), (-3,-3), (-1,-3)
5) Vertices after 90° CW rotation: (-2,3), (-1,3), (-1,2), (1,2), (1,1), (-2,1)
6) Vertices after 90° CCW rotation: (-2,2), (-4,2), (-4,3), (-3,3), (-3,4), (-2,4)