Question

if the points(x,y)be equidistant from the points(6,-1)and(2,3) prove that x-y is equal to 3

Answer 1

A(6,-1). B(x,y). C(2,3)
AB=BC
√[(x-6)²+(y+1)²] =√[(x-2)²+(y-3)²
(x-6)²+(y+1)²=(x-2)²+(y-3)²
x²+y²+36+1+2y-12x=x²+y²+4+9-6y-4x
37+2y-12x=13-6y-4x
37-13=12x-4x-6y-2y
24=8(x-y)
Hence,
x-y=3