# How do you find the value of a given the points (8,-2), (5,a) with a distance of 3?

$a = - 2$
distance d between two points $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$ is given by : $d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
$9 = {\left(5 - 8\right)}^{2} + {\left(a + 2\right)}^{2}$
$a = - 2$