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

Question

Accepted Answer

Step 1: $PA^2 = PB^2 \Rightarrow (x - 5)^2 + (y - 1)^2 = (x - 1)^2 + (y - 5)^2$
Step 2: $x^2 - 10x + 25 + y^2 - 2y + 1 = x^2 - 2x + 1 + y^2 - 10y + 25$
$\Rightarrow -10x - 2y = -2x - 10y \Rightarrow 8y = 8x \Rightarrow x = y$

Question

Solution