Let’s solve each rotation problem step by step. We’ll use the origin (0,0) as the center of rotation unless otherwise stated. Remember:
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90° counterclockwise: (x, y) → (-y, x)
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180°: (x, y) → (-x, -y)
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270° counterclockwise =
90° clockwise: (x, y) → (y, -x)
We’ll apply these rules to each figure’s vertices.
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Problem 1: Rotate 180° about the origin
Original points (from grid):
- A(1, 3)
- B(4, 2)
- C(3, -1)
- D(-1, 1)
Apply 180° rule: (x, y) → (-x, -y)
- A’(–1, –3)
- B’(–4, –2)
- C’(–3, 1)
- D’(1, –1)
Plot these new points and connect them in order.
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Problem 2: Rotate 270° about the origin
This is same as 90° clockwise: (x, y) → (y, -x)
Original points:
- P(2, 2)
- Q(5, 1)
- R(4, -1)
Apply rule:
- P’(2, -2)
- Q’(1, -5)
- R’(-1, -4)
Plot and connect.
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Problem 3: Rotate 90° counterclockwise about the origin
Rule: (x, y) → (-y, x)
Original points:
- S(-3, 1)
- T(-2, 4)
- U(-1, 2)
Apply:
- S’(-1, -3)
- T’(-4, -2)
- U’(-2, -1)
Plot and connect.
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Problem 4: Rotate 90° clockwise about the origin
Same as 270° CCW: (x, y) → (y, -x)
Original points:
- V(3, 1)
- W(4, 4)
- X(1, 3)
Apply:
- V’(1, -3)
- W’(4, -4)
- X’(3, -1)
Plot and connect.
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Problem 5: Rotate 90° clockwise about the origin
Again: (x, y) → (y, -x)
Original points:
- Y(1, -2)
- Z(4, -1)
- AA(3, -4)
Apply:
- Y’(-2, -1)
- Z’(-1, -4)
- AA’(-4, -3)
Plot and connect.
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Problem 6: Rotate 180° about the origin
Rule: (x, y) → (-x, -y)
Original points:
- BB(2, -1)
- CC(4, -2)
- DD(3, -4)
Apply:
- BB’(-2, 1)
- CC’(-4, 2)
- DD’(-3, 4)
Plot and connect.
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Final Answer:
For each problem, plot the transformed coordinates using the rotation rules above. The final images are the polygons formed by connecting the rotated vertices in the same order as the original figures.
Parent Tip: Review the logic above to help your child master the concept of rotation worksheet.
