Question

Which point on x- axis is equidistant from (5, 9) and (-4 , 6) ?

Answer 1

Any point on x-axis is of the form, (x,0)
It is equidistant from (5,9) and (-4,6)

Distance of (x,0) from (5,9) =
=​​​​​​$\sqrt{(}5-x{)}^2+9^2$ ---- (i)

Distance of (x,0) from (-4,6)=
= $\sqrt{(}x+4{)}^2+6^2$ ----- (ii)

(i) = (ii)

$\sqrt{(}5-x{)}^2+9^2$ ​​​​​​​= $\sqrt{(}x+4{)}^2+6^2$ ​​​​​​​
$25+x^2-10x+81=x^2+16+8x+36$

$106-52=18x$

$54=18x$

$x=3$
(3,0) is the equidistant point.