Question

Find m if the point on the $x$-axis which is equidistant from $(7,6)$ and $(3,4)$ is $(\frac{m}{2},0)$

Answer 1

$A(7,6),B(3,4),O(\frac{m}{2},0)$

$AO=BO\Rightarrow {AO}^2={BO}^2$

By distance formula $\Rightarrow {(7-\frac{m}{2})}^2+6^2={(3-\frac{m}{2})}^2+4^2$

$\Rightarrow m=15$