# How do you find the value of a given the points (4,a), (1,6) with a distance of 5?

Jul 27, 2016

$a = 10 \mathmr{and} a = 2$

#### Explanation:

Use the distance formula and substitute the values you know:

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

5 = sqrt[(4-1)^2 +(a-6)^2

$5 = \sqrt{{3}^{2} + {\left(a - 6\right)}^{2}} \text{ square both sides}$

$25 = 9 + \left({a}^{2} - 12 a + 36\right) \text{ quadratic = 0}$

$0 = {a}^{2} - 12 a + 36 + 9 - 25$

$0 = {a}^{2} - 12 a + 20$

$0 = \left(a - 10\right) \left(a - 2\right)$
$a = 10 \mathmr{and} a = 2$