a point is equidistant from A(-6,4) and B(2,-8) find its coordinates if the abscissa and ordinate are equal - Maths - Coordinate Geometry

Question

a point is equidistant from A(-6,4) and B(2,-8) find its
coordinates if the abscissa and ordinate are equal

Ruchira Banka · Accepted Answer

Let coordinates of ‘P’ be
(x, x)

A (-6, 4) and B (2, -8)

Since PA = PB

PA2= PB2

Using distance formula,

(x+6)2+ (x-4)2= (x-2)2+(x+8)2x2+36+12x +x2 +16-8x =x2+4-4x +x2+64
+16x2x2+4x+52 = 2x2+12x+684x-12x = 68-52-8x
=16x=-168=-2

Therefore, the coordinates of P are (-2,
-2)

a point is equidistant from A(-6,4) and B(2,-8).find its coordinates if the abscissa and ordinate are equal.