Question: (a) Draw a coordinate system in the plane. Show that points (3, 1) and (1, 3) are symmetric about the line y = x, and the same for (5, 3) and (3, 5).
(b) Use properties of congruent triangles to prove that points (a, b) and (b, a) in the plane are symmetric about the line y = x. What is the point half-way between these two points?