Question
(5,6) rotat 270 on a graph
Answers
GPT-4o mini
To rotate the point (5, 6) by 270 degrees around the origin (0, 0) on a graph, you can use the following method:
1. **Understand the rotation**: Rotating a point 270 degrees counterclockwise is equivalent to rotating it 90 degrees clockwise.
2. **Apply the rotation**: The formulas to rotate a point (x, y) by an angle θ are:
- \( x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \)
- \( y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \)
For a 90 degrees clockwise rotation, the values of cosine and sine are:
- \( \cos(90^\circ) = 0 \)
- \( \sin(90^\circ) = 1 \)
Thus, the formulas become:
- \( x' = y \)
- \( y' = -x \)
3. **Calculate the rotated coordinates**:
- For the point (5, 6):
- \( x' = 6 \)
- \( y' = -5 \)
4. **Final result**: The coordinates of the point (5, 6) after a 270-degree rotation around the origin are (6, -5).
1. **Understand the rotation**: Rotating a point 270 degrees counterclockwise is equivalent to rotating it 90 degrees clockwise.
2. **Apply the rotation**: The formulas to rotate a point (x, y) by an angle θ are:
- \( x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \)
- \( y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \)
For a 90 degrees clockwise rotation, the values of cosine and sine are:
- \( \cos(90^\circ) = 0 \)
- \( \sin(90^\circ) = 1 \)
Thus, the formulas become:
- \( x' = y \)
- \( y' = -x \)
3. **Calculate the rotated coordinates**:
- For the point (5, 6):
- \( x' = 6 \)
- \( y' = -5 \)
4. **Final result**: The coordinates of the point (5, 6) after a 270-degree rotation around the origin are (6, -5).