Question

A triangle has vertices W(−3,7) ,Q(1,−1) , and Z(−5,−2) . Apply rotation mapping rules to find the coordinates of W′ after a 90-degree (counterclockwise) rotation about the origin

W′ (Answer,here)

Answer 1

To rotate a point \( (x, y) \) by 90 degrees counterclockwise about the origin, the formula used is:

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

Given the vertex \( W(-3, 7) \):

1. Identify \( x \) and \( y \):
- \( x = -3 \)
- \( y = 7 \)

2. Apply the rotation formula:
- New \( x \) = \( -y = -7 \)
- New \( y \) = \( x = -3 \)

Thus, the coordinates of \( W' \) after the rotation are:

\[
W' = (-7, -3)
\]

So, the answer is:

\[
W' = (-7, -3)
\]