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. (1 point)

Answer 1

To rotate a point \((x, y)\) by 90 degrees counterclockwise about the origin, the new coordinates \((x', y')\) can be found using the following transformation rules:

\[
(x', y') = (-y, x)
\]

Now, let's apply this to the point \(W (-4, 7)\).

1. **Identify the coordinates of W**:
- \(x = -4\)
- \(y = 7\)

2. **Apply the rotation rules**:
- For \(W'\), the new coordinates will be:
\[
x' = -y = -7
\]
\[
y' = x = -4
\]

3. **Combine the results**:
- The coordinates of \(W'\) after the rotation are:
\[
W' = (-7, -4)
\]

Thus, the coordinates of \(W'\) after a 90-degree rotation about the origin are \(\boxed{(-7, -4)}\).