The vertices of PQRS

Question

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:

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