Question

If the distances of the point p(x,y) from the points (6,-1) and (1,4) are equal, prove that x-y=20.

Answer 1

Using distance formula and cross-checking answer by section formula, the answer of x-y is 2, not 20.
(x-6)^(2) + (y+1)^(2) = (x-1)^(2) + (y-4)^(2)
Solving this, x-y = 2

Again, by section formula: (m.x1 + n.x2)/(m +n) = x and same way for y.
Since, both distances are equal m = n = 1
x = 7/2
y = 3/2
x-y= 4/2 = 2