Question
(5,4) 270 clockwise
Answers
GPT-4o mini
To rotate the point (5, 4) 270 degrees clockwise around the origin, you can follow these steps:
1. **Convert the rotation angle**: 270 degrees clockwise is equivalent to a 90 degrees counterclockwise rotation.
2. **Apply the rotation formula**: The formulas for rotating a point (x, y) around the origin by an angle θ are:
- x' = x * cos(θ) - y * sin(θ)
- y' = x * sin(θ) + y * cos(θ)
For 90 degrees counterclockwise:
- cos(90°) = 0
- sin(90°) = 1
3. **Substitute the values**:
- For (5, 4):
- x' = 5 * 0 - 4 * 1 = -4
- y' = 5 * 1 + 4 * 0 = 5
4. **Result**: After rotating (5, 4) by 270 degrees clockwise (or equivalently 90 degrees counterclockwise), the new coordinates are (-4, 5).
So, the point (5, 4) after a 270-degree clockwise rotation becomes **(-4, 5)**.
1. **Convert the rotation angle**: 270 degrees clockwise is equivalent to a 90 degrees counterclockwise rotation.
2. **Apply the rotation formula**: The formulas for rotating a point (x, y) around the origin by an angle θ are:
- x' = x * cos(θ) - y * sin(θ)
- y' = x * sin(θ) + y * cos(θ)
For 90 degrees counterclockwise:
- cos(90°) = 0
- sin(90°) = 1
3. **Substitute the values**:
- For (5, 4):
- x' = 5 * 0 - 4 * 1 = -4
- y' = 5 * 1 + 4 * 0 = 5
4. **Result**: After rotating (5, 4) by 270 degrees clockwise (or equivalently 90 degrees counterclockwise), the new coordinates are (-4, 5).
So, the point (5, 4) after a 270-degree clockwise rotation becomes **(-4, 5)**.