Step 1 :Given the triangle with vertices at points P(-2, 1), Q(4, 1), and R(4, -3), we are asked to find the image of the triangle under a 90 degree rotation about the origin.
Step 2 :The transformation rule for a 90 degree rotation about the origin is \((x, y) \rightarrow (-y, x)\). This means that we replace each x-coordinate with the negative of the y-coordinate and each y-coordinate with the x-coordinate.
Step 3 :Applying the transformation rule to point P(-2, 1), we get P'(-1, -2).
Step 4 :Applying the transformation rule to point Q(4, 1), we get Q'(-1, 4).
Step 5 :Applying the transformation rule to point R(4, -3), we get R'(3, 4).
Step 6 :The image of the triangle under a 90 degree rotation about the origin is given by the points P'(-1, -2), Q'(-1, 4), and R'(3, 4).
Step 7 :Final Answer: \(\boxed{P'(-1, -2), Q'(-1, 4), R'(3, 4)}\)