# Find the values of x for which the distance between

Question:

Find the values of x for which the distance between the point P(2, −3), and Q (x, 5) is 10.

Solution:

It is given that distance between $P(2,-3)$ and $Q(x, 5)$ is 10 .

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,

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

So,

$10^{2}=(x-2)^{2}+(5+3)^{2}$

On further simplification,

$(x-2)^{2}=36$

$x=2 \pm 6$

$=8,-4$