**Q) **Point P(x, y) is equidistant from points A(5, 1) and B(1,5). Prove that x = y.

**Ans: **Let’s draw the diagram to solve:

Given that PA = PB

Hence, PA^{2 }= PB^{2}

(x – 5)^{2 }+ (y – 1)^{2} = (x – 1)^{2} + (y – 5)^{2}

– 10 x – 2y = – 2 x – 10 y

– 8 x = – 8 y

x = y ……………………….**Hence Proved **