# How do you find the possible values for a if the points (6,a), (5,0) has a distance of sqrt17?

Apr 3, 2017

$a = - 4$ or $a = 4$

#### Explanation:

The distance between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is

$\sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

Hence, distance between two points $\left(6 , a\right)$ and $\left(5 , 0\right)$ is

$\sqrt{{\left(5 - 6\right)}^{2} + {\left(0 - a\right)}^{2}}$ and this should be $\sqrt{17}$

Therefore $\sqrt{{\left(5 - 6\right)}^{2} + {\left(0 - a\right)}^{2}} = \sqrt{17}$

or ${\left(5 - 6\right)}^{2} + {\left(0 - a\right)}^{2} = 17$

i.e. $1 + {a}^{2} = 17$

or ${a}^{2} - 16 = 0$

or $\left(a + 4\right) \left(a - 4\right) = 0$

i.e. $a = - 4$ or $a = 4$