Question

Is △P’Q’R’ a 180° rotation about the origin of △PQR? Explain.

Answer 1

Yes, △P’Q’R’ is a 180° rotation about the origin of △PQR.

Step-by-step explanation:

Yes, △P’Q’R’ is a 180° rotation about the origin of △PQR. To prove this, we need to show that the coordinates of P’, Q’, and R’ can be expressed in terms of the coordinates of P, Q, and R using the given rotation formula:

x' = x cos q + y sin o

y' = -x sin p + y cos p

Using this formula, we can calculate the new coordinates of P’, Q’, and R’, and see that they are indeed obtained by rotating the original triangle 180° around the origin.