Question

Find the point on x-axis which is equidistant from $(2,-5)$ and $(-2,9)$.

Answer 1

Let the point on the $x$-axis be B$\left(x,0\right)$.

The point is equidistance from the point A$\left(2,-5\right)$ and C$\left(-2,9\right)$.

Then,

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

$\sqrt{{\left(x-2\right)}^2+{\left(0+5\right)}^2}=\sqrt{{\left(x+2\right)}^2+{\left(0-9\right)}^2}$

$x^2-4x+4+25=x^2+4x+4+81$

$-8x=56$

$x=-7$

The point on the $x$ axis is $\left(-7,0\right)$.