Question

If distance of point P(x,y) from point A(6,-1) and B(1,4) are equal, prove that x-y=20

Answer 1

Here, point P is midpoint of points A and B.
By Midpoint formula,
$x = \frac{x1 + x2}{2}$

$x = \frac{6 + 1}{2} = \frac{7}{2}$

$y = \frac{ 4 + ( - 1)}{2} = \frac{3}{2}$

$x - y = \frac{7}{2} - \frac{3}{2} = \frac{7 - 3}{2 }$
$= 2$