If the point P(x,y) is equidistant from the points A(5,1) and B(1,5), prove that x=y.

If the point P(x,y) is equidistant from the points A(5,1) and B(1,5),

1.	If the point P(x,y) is equidistant from the points A(5,1) and B(1,5), prove that x=y.
Answer» PA = PB (Given){tex}\\therefore {/tex}\xa0PA2 = PB2{tex} \\Rightarrow {/tex}\xa0(5 - x)2 + (1 - y)2 = (1 - x)2 + (5 - y)2{tex} \\Rightarrow {/tex}\xa025 + x2 - 10x + 1 + y2 - 2y = 1 + x2 - 2x + 25 + y2 - 10y{tex} \\Rightarrow {/tex}\xa0-8x = -10y + 2y{tex} \\Rightarrow {/tex}\xa0-8x = -8y{tex} \\Rightarrow {/tex}\xa0x = y\xa0