Question

Find the co-ordinate of a points on $x$-axis which is equidistant from the points $(-2,5)$ and $(2,-3)$.

Answer 1

Distance between two points whose co-ordinates are $(x_1,y_1)$ and $(x_2,y_2)$ is given as,

$D=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

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

According to question

$\sqrt{{(x+2)}^2+{\left(5\right)}^2}=\sqrt{{(x-2)}^2+{\left(3\right)}^2}$

Squaring both sides

$(x+2{)}^2+25=(x-2{)}^2+9$

$x^2+4x+29=x^2-4x+13$

$8x=-16$

$x=-2$

Thus co-ordinates of required point are $(-2,0)$