Question

Use rotation mapping to locate after a -90 degree (clockwise) rotation about the origin. (1 point)
A'=(-2,-8)
A'=(2,-8)
A'=(2,8)
A'=(-2,8)

Answer 1

To locate a point after a -90 degree (clockwise) rotation about the origin, we can use the following rotation mapping formula:

For a point \((x, y)\):
- After a -90 degree rotation, the new coordinates \((x', y')\) will be given by:
\[
(x', y') = (y, -x)
\]

Let's apply this to the point \(A = (x, y)\):

1. We'll choose a point \(A = (2, 8)\) to demonstrate the rotation.
2. Applying the formula:
- Whenever \(x = 2\) and \(y = 8\), then after a -90 degree rotation:
- \(x' = y = 8\)
- \(y' = -x = -2\)

So, A' becomes:
\[
A' = (8, -2)
\]

Ultimately, we can apply this to the given points:
1. A' = (-2, -8) - does not satisfy
2. A' = (2, -8) - does not satisfy
3. A' = (2, 8) - does not satisfy
4. A' = (-2, 8) - does not satisfy

Thus, based on the requirement you’ve given and the rotation mapping, the actual logic gives us:
\[
A' = (8, -2).
\]

None of the provided options correspond to the expected results.