Question

Rectangle PQRS is rotated 90° clockwise about the origin.

On a coordinate plane, rectangle P Q R S has points (negative 3, negative 1), (negative 1, negative 1), (negative 1, negative 4), (negative 3, negative 4).

What are the coordinates of R’?
R’(4,–1)
R’(–4,1)
R’(1,4)
R’(–1,–4)

Answer 1

To find the new coordinates after rotating point R (which is located at (-1, -4)) 90° clockwise about the origin, we can use the rotation formula:

For a point (x, y), the new coordinates (x', y') after a 90° clockwise rotation are given by:
\[
(x', y') = (y, -x)
\]

Applying this to point R (-1, -4):
- The x-coordinate (-1) becomes y-coordinate (-4).
- The y-coordinate (-4) becomes -x-coordinate (1).

Thus, the new coordinates of R' after rotating 90° clockwise are:
\[
R' = (-4, 1)
\]

So the correct option for the coordinates of R’ is:
**R’(–4,1)**.