Question

Find the point on x- axis which is equidistant from the points (-2, 5) and (2, -3).

Answer 1

Let the point of x-axis be X (x,0)

Given : A( - 2 , 5) and B( 2 , - 3 ) are equidistant from P , So

AX = BX , Then

$A{X}^2$ = $B{X}^2$

Using distance formula ( - 2 , 5) and B( 2 , - 3 ) (x,0)

AX = $\sqrt{(-2-x{)}^2+(5-0{)}^2}$ (1)
BX = $\sqrt{(2-x{)}^2+(-3-0{)}^2}$ (2)
Squaring 1 and 2 and equating because AX = BX

4+4x+$x^2$ +25 = 4-4x+$x^2$ + 9

8x = -16

x = -2
Hence the point X on X- axis is (-2,0)