Question

Rotate the point (-3, -5) on a geometric figure 270 dergees counterclockwise. What the is the new point

Answer 1

To rotate the point \((-3, -5)\) by 270 degrees counterclockwise, we can use the rotation formula. The 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.

The standard rotation formulas for a point \((x, y)\) are:
- 90 degrees counterclockwise: \((-y, x)\)
- 180 degrees: \((-x, -y)\)
- 270 degrees counterclockwise (or 90 degrees clockwise): \((y, -x)\)

For our point \((-3, -5)\):
1. The \(x\) value is \(-3\).
2. The \(y\) value is \(-5\).

Using the formula for 270 degrees counterclockwise (90 degrees clockwise), we substitute:
\[
(x, y) \to (y, -x) = (-5, 3)
\]

Thus, the new point after rotating \((-3, -5)\) by 270 degrees counterclockwise is \((-5, 3)\).