Question

The coordinates of PQR are P(-3, 2), Q(2, 5), and R(0, 0). After applying r(270,O), what are the coordinates of Q'?

Answer 1

After applying a 270-degree rotation about the origin to point Q with coordinates (2, 5), the new coordinates of Q' are (-5, 2).

Step-by-step explanation:

The question is concerned with coordinate transformation, specifically applying a 270-degree rotation about the origin, denoted as r(270,O), to a point in the Cartesian plane. Here we focus on finding the new coordinates of point Q after the rotation. In the Cartesian coordinate system, a 270-degree (or -90-degree) rotation about the origin can be understood as swapping the x and y values of a point's coordinates and changing the sign of the new x-coordinate. The generic formula to calculate the new position, Q', of a point Q(x, y) after a 270-degree rotation about the origin is given by Q'(-y, x).

For point Q with coordinates (2, 5), applying this transformation formula results in Q'(-5, 2). Therefore, after a 270-degree rotation about the origin, the coordinates of Q' become (-5, 2).