Question

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

Answer 1

Let the point on x-axis $=(x,0)$

Given: The points is equidistant from $(2,-5)$ and $(-2,9)$

$\Rightarrow$ Distance between $(2,-5)$ & $(x,0)=$ distance between $(x,0)$ & $(-2,9)$

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

Squaring both sides, we get

$(x-2{)}^2+25=(x+2{)}^2+81$

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

$-4x-4x=81-25$

$-8x=56$

$x=\frac{56}{-8}=-7$

$\therefore x=-7$

$\therefore$ Point in x-axis equidistant from $(2,-5)$ & $(-2,9)$ is $(-7,0)$.