Polygon PSRT is drawn with vertices at P(1, 5), S(1, 0), R(−2, −3), T(−4, 2). Determine the image vertices of R′ if the preimage is rotated 270° counterclockwise.

Question

R′(−3, 2)
R′(2, 3)
R′(3, −2)
R′(−2, −3)

Answer 1

To find the image of vertex R(−2, −3) after a 270° counterclockwise rotation around the origin, we can use the rotation formula for rotating a point \((x, y)\) by an angle θ:

Rotation of \((x, y)\) by 270° counterclockwise: \[ (x', y') = (y, -x) \]

Now, applying this rotation to the coordinates of R: \[ R(-2, -3) \rightarrow (y, -x) = (-3, -(-2)) = (-3, 2) \]

Therefore, the resulting image vertex \(R'\) after the rotation is \((-3, 2)\).

Thus, the correct answer is: R′(−3, 2).