Let’s solve each rotation problem step by step.
We are rotating shapes about the origin (0,0). Here’s how coordinates change:
-
90° clockwise: (x, y) → (y, -x)
-
180°: (x, y) → (-x, -y)
-
90° counterclockwise: (x, y) → (-y, x)
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Problem 1: 90° clockwise rotation
Original points from graph:
- A = (-4, 2)
- B = (1, 4)
- C = (-1, -2)
Apply rule: (x, y) → (y, -x)
A’ = (2, -(-4)) = (2, 4)
B’ = (4, -1)
C’ = (-2, -(-1)) = (-2, 1)
✔ Check:
A(-4,2) → (2,4) — correct
B(1,4) → (4,-1) — correct
C(-1,-2) → (-2,1) — correct
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Problem 2: 180° rotation
Original points:
- U = (-2, 4)
- V = (4, 4)
- W = (-3, 1)
Rule: (x, y) → (-x, -y)
U’ = (2, -4)
V’ = (-4, -4)
W’ = (3, -1)
✔ Check:
U(-2,4) → (2,-4) — correct
V(4,4) → (-4,-4) — correct
W(-3,1) → (3,-1) — correct
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Problem 3: 90° counterclockwise rotation
Original points:
- E = (1, 1)
- F = (5, 2)
- G = (4, 4)
- H = (2, 5)
Rule: (x, y) → (-y, x)
E’ = (-1, 1)
F’ = (-2, 5)
G’ = (-4, 4)
H’ = (-5, 2)
✔ Check:
E(1,1) → (-1,1) — correct
F(5,2) → (-2,5) — correct
G(4,4) → (-4,4) — correct
H(2,5) → (-5,2) — correct
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Problem 4: 180° rotation
Original points:
- P = (-2, 1)
- Q = (-2, -4)
- R = (3, -4)
Rule: (x, y) → (-x, -y)
P’ = (2, -1)
Q’ = (2, 4)
R’ = (-3, 4)
✔ Check:
P(-2,1) → (2,-1) — correct
Q(-2,-4) → (2,4) — correct
R(3,-4) → (-3,4) — correct
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Final Answer:
1.) A’(2, 4), B’(4, -1), C’(-2, 1)
2.) U’(2, -4), V’(-4, -4), W’(3, -1)
3.) E’(-1, 1), F’(-2, 5), G’(-4, 4), H’(-5, 2)
4.) P’(2, -1), Q’(2, 4), R’(-3, 4)
Parent Tip: Review the logic above to help your child master the concept of rotation worksheet.
