Question

The vertices of PQRS
have coordinates P(−1, 5)
, Q(2, −4)
, R(3, 4)
, and S(−3, −2)
on a coordinate plane. What are the coordinates of the vertices after a counterclockwise rotation 90°
about the origin? Enter the answers.

Answer 1

To perform a counterclockwise rotation of 90° about the origin, you can use the following transformation for each vertex \((x, y)\):

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

Now, applying this transformation to each vertex:

1. For vertex \(P(-1, 5)\):
\[
P' = (-5, -1)
\]

2. For vertex \(Q(2, -4)\):
\[
Q' = (4, 2)
\]

3. For vertex \(R(3, 4)\):
\[
R' = (-4, 3)
\]

4. For vertex \(S(-3, -2)\):
\[
S' = (2, -3)
\]

So, the coordinates of the vertices after a counterclockwise rotation of 90° about the origin are:

- \(P'(-5, -1)\)
- \(Q'(4, 2)\)
- \(R'(-4, 3)\)
- \(S'(2, -3)\)