# Find all possible values of x for which the distance between the points

Question:

Find all possible values of x for which the distance between the points A(x, −1) and B(5, 3) is 5 units.

Solution:

Given AB = 5 units
Therefore, (AB)2 = 25 units

$\Rightarrow(5-x)^{2}+\{3-(-1)\}^{2}=25$

$\Rightarrow(5-x)^{2}+(3+1)^{2}=25$

$\Rightarrow(5-x)^{2}+(4)^{2}=25$

$\Rightarrow(5-x)^{2}+16=25$

$\Rightarrow(5-x)^{2}=25-16$

$\Rightarrow(5-x)^{2}=9$

$\Rightarrow(5-x)=\pm \sqrt{9}$

$\Rightarrow 5-x=\pm 3$

$\Rightarrow 5-x=3$ or $5-x=-3$

$\Rightarrow x=2$ or 8

Therefore, x = 2 or 8.