# How do you find the distance between points (5,2), (3,-3)?

Apr 13, 2017

Basically use the formula ${a}^{2} + {b}^{2} = {c}^{2}$. where
$a = \text{the change in } x ,$
$b = \text{ the change in } y$
$c = \text{the distance between them. }$

#### Explanation:

$x$ and $y$ form the legs of a ninety degree triangle so the equation
${a}^{2} + {b}^{2} = {c}^{2}$can be used to find the distance between the two points.

The length of the $x$ line can be found by subtracting the two values for $x$ in the two points

${x}_{1} - {x}_{2} = a$

$5 - 3 = 2$ so, $a$ the distance for $x$ is 2

The length of the $y$ line can be found by subtracting the two values for $y$ in the two points

${y}_{1} - {y}_{2} = b$

$2 - \left(- 3\right) = 5$ so, $b$ the distance for $y$ is 5

${2}^{2} + {5}^{2} = {c}^{2}$

$4 + 25 = {c}^{2}$

$29 = {c}^{2}$

$\sqrt{29} = {\sqrt{c}}^{2}$

$5.4 = c$