(-7,2) rotated 270 degrees clockwise around the origin

Answer 1

To rotate the point \((-7, 2)\) 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 formulas: The rotation of a point \((x, y)\) counterclockwise by an angle \(\theta\) around the origin can be calculated using: \[ x' = x \cos(\theta) - y \sin(\theta) \] \[ y' = x \sin(\theta) + y \cos(\theta) \] For a 90-degree counterclockwise rotation, \(\theta = 90^\circ\), so: \[ \cos(90^\circ) = 0 \quad \text{and} \quad \sin(90^\circ) = 1 \]

3. Plug in the values: \[ x' = -7 \cdot 0 - 2 \cdot 1 = -2 \] \[ y' = -7 \cdot 1 + 2 \cdot 0 = -7 \]

So, after rotating the point \((-7, 2)\) 270 degrees clockwise around the origin, the new coordinates are \((-2, -7)\).