Question

Rotate the point (−4, −6) on a geometric figure. What is the new coordinate?

Answer 1

To determine the new coordinates of the point \((-4, -6)\) after a rotation, we need to specify the angle of rotation and the center of rotation.

Common rotation angles include:

- 90 degrees counterclockwise
- 180 degrees
- 90 degrees clockwise

Here are the transformations for these common rotations around the origin (0, 0):

1. **90 degrees counterclockwise**:
\[
(x, y) \rightarrow (-y, x)
\]
So, \((-4, -6)\) becomes \((6, -4)\).

2. **180 degrees**:
\[
(x, y) \rightarrow (-x, -y)
\]
So, \((-4, -6)\) becomes \((4, 6)\).

3. **90 degrees clockwise**:
\[
(x, y) \rightarrow (y, -x)
\]
So, \((-4, -6)\) becomes \((-6, 4)\).

If you can provide the angle and center of rotation, I can give you the exact new coordinates after the rotation!