# If the distance between points (x, 0)

Question:

If the distance between points (x, 0) and (0, 3) is 5, what are the values of x?

Solution:

We have to find the unknown $x$ using the distance between $\mathrm{A}(x, 0)$ and $\mathrm{B}(0,3)$ which is $5 .$ In general, the distance between $\mathrm{A}\left(x_{1}, y_{1}\right)$ and $\mathrm{B}\left(x_{2}, y_{2}\right)$ is given by,

$\mathrm{AB}=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

So,

$5=\sqrt{(x-0)^{2}+(0-3)^{2}}$

Squaring both the sides we get,

$x^{2}-16=0$

$\mathrm{SO}$,

$x=\pm 4$