# The distance between (x, 2) and (0,6) is 5 units. What is the value of x?

The distance between the two points is

$d = \sqrt{{\left(x - 0\right)}^{2} + {\left(2 - 6\right)}^{2}} = \sqrt{{x}^{2} + 16}$

Hence

$\sqrt{{x}^{2} + 16} = 5$

${x}^{2} + 16 = 25$

${x}^{2} = 9$

$x = \pm 3$