Question

If P(x, y) is point equidistant from the points A(6, –1) and B(2, 3), show that x – y = 3.

Answer 1

The given points are A(6,-1) and B(2,3). The point P(x, y) equidistant from the points A and B So, PA = PB

Also,` (PA)^2 = (PB)^2`

`⇒ (6-x)^2 +(-1-y)^2 = (2-x) ^2 +(3-y)^2`

`⇒ x^2-12x +36+y^2+2y+1=x^2-4x+4+y^2-6y+9`

`⇒x^2 +y^2-12 x +2y +37 = x^2 -4x-6y+13`

`⇒ x^2 +y^2 -12x +2y -x^2 -y^2 +4x +6y = 13-37`

⇒ -8x +8y = -24

⇒-8 (x-y) = -24 

`⇒x-y =(-24)/(-8)`

`⇒ x-y = 3`

Hence proved