Question
What is (1, 2) rotated 270 degrees clockwise
Answers
GPT-4o mini
To rotate the point \((1, 2)\) by 270 degrees clockwise, you can follow these steps:
1. **Understand the rotation**: A 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation. So we can proceed with that instead.
2. **Use the rotation formula**: The formula for rotating a point \((x, y)\) counterclockwise by \(\theta\) degrees is:
\[
(x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta)
\]
For a 90-degree counterclockwise rotation, \(\theta = 90^\circ\), which gives \(\cos 90^\circ = 0\) and \(\sin 90^\circ = 1\).
3. **Apply the rotation**: For the point \((1, 2)\):
\[
x' = 1 \cdot 0 - 2 \cdot 1 = 0 - 2 = -2
\]
\[
y' = 1 \cdot 1 + 2 \cdot 0 = 1 + 0 = 1
\]
4. **Result**: The coordinates of the point \((1, 2)\) after a 270-degree clockwise rotation are \((-2, 1)\).
Thus, \((1, 2)\) rotated 270 degrees clockwise is \((-2, 1)\).
1. **Understand the rotation**: A 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation. So we can proceed with that instead.
2. **Use the rotation formula**: The formula for rotating a point \((x, y)\) counterclockwise by \(\theta\) degrees is:
\[
(x', y') = (x \cos \theta - y \sin \theta, x \sin \theta + y \cos \theta)
\]
For a 90-degree counterclockwise rotation, \(\theta = 90^\circ\), which gives \(\cos 90^\circ = 0\) and \(\sin 90^\circ = 1\).
3. **Apply the rotation**: For the point \((1, 2)\):
\[
x' = 1 \cdot 0 - 2 \cdot 1 = 0 - 2 = -2
\]
\[
y' = 1 \cdot 1 + 2 \cdot 0 = 1 + 0 = 1
\]
4. **Result**: The coordinates of the point \((1, 2)\) after a 270-degree clockwise rotation are \((-2, 1)\).
Thus, \((1, 2)\) rotated 270 degrees clockwise is \((-2, 1)\).