What is (1, 2) rotated 270 degrees clockwise

Answer 1

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 \((-2, 1)\).