Question

The triangle ABC in the plane has vertices A(1, 0), B(3, 1), C(2, 2). The triangle PQR has vertices P(−1, 0), Q(−3, 1), R(−2, 2). Draw a rough sketch of the two triangles, and by explicitly describing an isometry between them (or otherwise), show that the triangles ABC and PQR are congruent.

Answer 1

I've drawn the sketch, I just don't understand what to do for "by explicitly describing an isometry between them (or otherwise), show that the triangles ABC and PQR are congruent."

Answer 2

An isometry is the way you map a point on a figure to the corresponding point on a congruent figure. If your sketch is correct, you'll see that the two triangles are reflections of each other across the y-axis. So you can use that as the expicit description, or as a general rule (not just for veticies) *any* point (x,y) on firgure 1 maps such that \[(x,y)\rightarrow(-x,y)\]
on figure 2.