# How do you find the value of a given the points (6,-7), (a,-4) with a distance of sqrt18?

Jul 24, 2016

$a = 3$ or $a = 9$

#### Explanation:

Calling ${p}_{1} = \left\{6 , - 7\right\}$ and ${p}_{2} = \left\{a , - 4\right\}$ the distance $d$ between
${p}_{1}$ and ${p}_{2}$ is obtained using Pitagoras.

$d = \sqrt{{\left(6 - a\right)}^{2} + {\left(- 7 + 4\right)}^{2}} = \sqrt{18}$

Squaring both sides

${\left(6 - a\right)}^{2} + {\left(- 7 + 4\right)}^{2} = 18$

developing results

${a}^{2} - 12 a + 27 = 0$

Solving for $a$ we obtain two solutions

$a = 3$ and $a = 9$