Question
(5,8) 270 degree rotation
Answers
GPT-4o mini
To rotate the point (5, 8) by 270 degrees counterclockwise around the origin, you can use the following method:
1. **Understanding 270 degrees rotation**: A 270-degree rotation counterclockwise is equivalent to a 90-degree rotation clockwise.
2. **Using rotation formulas**: The rotation of a point (x, y) by an angle θ can be obtained using the following formulas:
- \( x' = x \cos(\theta) - y \sin(\theta) \)
- \( y' = x \sin(\theta) + y \cos(\theta) \)
For 270 degrees counterclockwise (or -90 degrees), the cosine and sine values are:
- \( \cos(270^\circ) = 0 \)
- \( \sin(270^\circ) = -1 \)
3. **Applying the formulas**:
- Using the point (5, 8):
\[
x' = 5 \cdot 0 - 8 \cdot (-1) = 0 + 8 = 8
\]
\[
y' = 5 \cdot (-1) + 8 \cdot 0 = -5 + 0 = -5
\]
So, after a 270-degree rotation counterclockwise around the origin, the new coordinates of the point (5, 8) will be (8, -5).
1. **Understanding 270 degrees rotation**: A 270-degree rotation counterclockwise is equivalent to a 90-degree rotation clockwise.
2. **Using rotation formulas**: The rotation of a point (x, y) by an angle θ can be obtained using the following formulas:
- \( x' = x \cos(\theta) - y \sin(\theta) \)
- \( y' = x \sin(\theta) + y \cos(\theta) \)
For 270 degrees counterclockwise (or -90 degrees), the cosine and sine values are:
- \( \cos(270^\circ) = 0 \)
- \( \sin(270^\circ) = -1 \)
3. **Applying the formulas**:
- Using the point (5, 8):
\[
x' = 5 \cdot 0 - 8 \cdot (-1) = 0 + 8 = 8
\]
\[
y' = 5 \cdot (-1) + 8 \cdot 0 = -5 + 0 = -5
\]
So, after a 270-degree rotation counterclockwise around the origin, the new coordinates of the point (5, 8) will be (8, -5).