Mathematics worksheet on rotation for secondary 2 students, featuring problems on 90° clockwise, 90° counterclockwise, and 180° rotations of shapes about the origin.

Let’s solve each rotation problem step by step. We’ll use the rules for rotating points around the origin (0,0):

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Rotation Rules:

- 90° clockwise:
(x, y) → (y, -x)

- 180° rotation (either direction):
(x, y) → (-x, -y)

- 90° counterclockwise:
(x, y) → (-y, x)

We’ll apply these to each point in each question.

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Problem 1: 90° clockwise rotation

Original points from graph:

- A is at (-4, 2)
- B is at (1, 4)
- C is at (-1, -2)

Apply rule: (x, y) → (y, -x)

→ A’ = (2, -(-4)) = (2, 4)
Wait — let’s double-check:
Rule: (x, y) → (y, -x)
So for A(-4, 2):
new x = y = 2
new y = -x = -(-4) = 4
→ A’(2, 4)

B(1, 4):
new x = 4
new y = -1
→ B’(4, -1)

C(-1, -2):
new x = -2
new y = -(-1) = 1
→ C’(-2, 1)

✔ Check: All look correct.

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Problem 2: 180° rotation

Original points:

- U is at (-2, 4)
- V is at (4, 4)
- W is at (-3, 1)

Rule: (x, y) → (-x, -y)

U’ = (2, -4)
V’ = (-4, -4)
W’ = (3, -1)

✔ Simple sign flip — looks good.

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Problem 3: 90° counterclockwise rotation

Original points:

- E is at (1, 1)
- F is at (5, 2)
- G is at (4, 4)
- H is at (2, 5)

Rule: (x, y) → (-y, x)

E(1,1) → (-1, 1)
F(5,2) → (-2, 5)
G(4,4) → (-4, 4)
H(2,5) → (-5, 2)

✔ Double-checked — yes, swap and negate first coordinate.

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Problem 4: 180° rotation

Original points:

- P is at (-2, 1)
- Q is at (-2, -4)
- R is at (3, -4)

Rule: (x, y) → (-x, -y)

P’ = (2, -1)
Q’ = (2, 4)
R’ = (-3, 4)

✔ Sign flips only — 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)