Given points A(2,-5),B(-2,9)
Let P(x,0) be the point on X-axis
which is equidistant from A and B i.e. PA=PB
Distance formula = √((x2 - x1)2 + (y2 - y1)2)
PA=√((-x)2 + (--0)2)
=√x2-√4x + +
=√x2-√4x +
PB=√(--x)2 + (-0)2
=√x2 + 4x + +
=√x2 + 4x +
But PA=PB
√x2-√4x + = √x2 + 4x +
Squaring on both sides we get
x2-4x+ = x2+4x+
-4x-4x=-
-8x=
x=-
(x,0)=(-,0) is the point which is equidistant from the given points.