Question

A triangle has vertices W (-4,7), Q (-1,-1) and Z (-7,-2). Apply rotation mapping rules to find the coordinates of W' after a 90-degree rotation about the origin.

Answer 1

To find the coordinates of the point W' after a 90-degree counterclockwise rotation about the origin, we can use the rotation mapping rule for 90 degrees, which states:

\[
(x, y) \rightarrow (-y, x)
\]

Given the coordinates of point W as (-4, 7), we can apply the rotation rule:

1. Take the y-coordinate (7) and make it the new x-coordinate.
2. Take the x-coordinate (-4) and make it the new y-coordinate, but negate it.

So:

- The original coordinates of W are (-4, 7).
- After applying the rotation:
- New x-coordinate: -y = -7
- New y-coordinate: x = -4

Thus, the coordinates of W' after a 90-degree rotation about the origin are:

\[
W' = (-7, -4)
\]