Rotations Worksheet - TheWorksheets.CoM - TheWorksheets Library - Free Printable

You're working on Rotations Worksheet 1, which asks you to find the new coordinates of given points after rotating them about the origin (0,0) by specific angles: 180°, 90° counterclockwise, and 90° clockwise.

Let’s go through each problem one by one. First, we’ll identify the original coordinates of each point from the grid, then apply the rotation rules.

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🔄 Rotation Rules (about the origin):

- 180° rotation:
`(x, y) → (-x, -y)`
*Every point flips to the opposite quadrant.*

- 90° counterclockwise rotation:
`(x, y) → (-y, x)`
*Example: (2,3) → (-3,2)*

- 90° clockwise rotation:
`(x, y) → (y, -x)`
*Example: (2,3) → (3,-2)*

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## ✔ Problem 1: Rotation 180° about the origin — Point H

Look at the grid:
Point H is at (4, -3)
*(4 units right, 3 units down)*

Apply 180° rule:
→ `(-4, 3)`

✔ Answer: (-4, 3)

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## ✔ Problem 2: Rotation 180° about the origin — Point D

Point D is at (-3, 2)
*(3 units left, 2 units up)*

Apply 180° rule:
→ `(3, -2)`

✔ Answer: (3, -2)

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## ✔ Problem 3: Rotation 90° counterclockwise about the origin — Point C

Point C is at (-2, -1)
*(2 left, 1 down)*

Apply 90° CCW rule: `(x, y) → (-y, x)`
→ `-(-1), -2` → `(1, -2)`

✔ Answer: (1, -2)

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## ✔ Problem 4: Rotation 90° counterclockwise about the origin — Point Y

Point Y is at (5, -1)
*(5 right, 1 down)*

Apply 90° CCW: `(x, y) → (-y, x)`
→ `-(-1), 5` → `(1, 5)`

✔ Answer: (1, 5)

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## ✔ Problem 5: Rotation 90° clockwise about the origin — Point N

Point N is at (-3, 2)
*(3 left, 2 up)*

Apply 90° CW: `(x, y) → (y, -x)`
→ `(2, -(-3))` → `(2, 3)`

✔ Answer: (2, 3)

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## ✔ Problem 6: Rotation 90° clockwise about the origin — Point V

Point V is at (-4, -2)
*(4 left, 2 down)*

Apply 90° CW: `(x, y) → (y, -x)`
→ `(-2, -(-4))` → `(-2, 4)`

✔ Answer: (-2, 4)

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## 📝 Final Answers:

1. H(4, -3) → (-4, 3)
2. D(-3, 2) → (3, -2)
3. C(-2, -1) → (1, -2)
4. Y(5, -1) → (1, 5)
5. N(-3, 2) → (2, 3)
6. V(-4, -2) → (-2, 4)

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💡 Tip for Visualizing Rotations:
- Imagine spinning the point around the origin like a Ferris wheel.
- For 180°, it’s like going straight across the center.
- For 90° CCW, think “left turn” — point moves to the next quadrant in counterclockwise direction.
- For 90° CW, think “right turn”.

Let me know if you’d like to see diagrams or practice more!