(-2,-2) rotated 270 degrees around the origin clockwise

Answer 1

To rotate the point \((-2, -2)\) 270 degrees clockwise around the origin, you can follow these steps:

1. Convert the clockwise rotation to a counterclockwise rotation: A 270-degree clockwise rotation is equivalent to a 90-degree counterclockwise rotation.

2. Use the rotation formula: For a counterclockwise rotation of a point \((x, y)\) by an angle \(\theta\), the new coordinates \((x', y')\) can be determined using the following formulas: \[ x' = x \cos(\theta) - y \sin(\theta) \] \[ y' = x \sin(\theta) + y \cos(\theta) \]

   For a 90-degree counterclockwise rotation: \(\cos(90^\circ) = 0\) and \(\sin(90^\circ) = 1\).

3. Apply the formulas: Using the point \((-2, -2)\): \[ x' = -2 \cdot 0 - (-2) \cdot 1 = 0 + 2 = 2 \] \[ y' = -2 \cdot 1 + (-2) \cdot 0 = -2 + 0 = -2 \]

The new coordinates after rotating \((-2, -2)\) 270 degrees clockwise around the origin are \((2, -2)\).