# How do you find the value of a given the points (a,2), (-3,3) with a distance of sqrt2?

Jul 26, 2017

$a = - 4 \mathmr{and} a = - 2$

#### Explanation:

Use the distance formula:

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

$\sqrt{2} = \sqrt{{\left(- 3 - a\right)}^{2} + {\left(3 - 2\right)}^{2}}$ $\to$ plug in given values

$\sqrt{2} = \sqrt{9 + 6 a + {a}^{2} + 1}$ $\to$ expand

$\sqrt{2} = \sqrt{{a}^{2} + 6 a + 10}$ $\to$ simplify

$2 = {a}^{2} + 6 a + 10$ $\to$ remove radical by squaring both sides

$0 = {a}^{2} + 6 a + 8$ $\to$ subtract $2$ from both sides

$0 = \left(a + 4\right) \left(a + 2\right)$ $\to$ factor

$0 = \left(a + 4\right) \mathmr{and} 0 = \left(a + 2\right)$ $\to$ there are two possible values for $a$

$a = - 4 \mathmr{and} a = - 2$