A right triangle has coordinates (-2,2) , (6,8) and (6,2). What is the perimeter of the triangle?

Jan 4, 2017

The perimeter of the triangle is 24

Explanation:

To find the perimeter of the triangle you need to find the distance between the three pairs of point.

(-2, 2) and (6, 8)
(-2, 2) and (6, 2)
(6, 2) and (6, 8)

The formula for calculating the distance between two points is:

$d = \sqrt{{\left(\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}\right)}^{2} + {\left(\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}\right)}^{2}}$

Calculating these three distances and then adding gives:

$p = \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{8} - \textcolor{b l u e}{2}\right)}^{2}} + \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{- 2}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{2}\right)}^{2}} + \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{8} - \textcolor{b l u e}{2}\right)}^{2}}$

$p = \sqrt{{\left(\textcolor{red}{6} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{8} - \textcolor{b l u e}{2}\right)}^{2}} + \sqrt{{\left(\textcolor{red}{6} + \textcolor{b l u e}{2}\right)}^{2} + {\left(\textcolor{red}{2} - \textcolor{b l u e}{2}\right)}^{2}} + \sqrt{{\left(\textcolor{red}{6} - \textcolor{b l u e}{6}\right)}^{2} + {\left(\textcolor{red}{8} - \textcolor{b l u e}{2}\right)}^{2}}$

$p = \sqrt{{8}^{2} + {6}^{2}} + \sqrt{{8}^{2} + {0}^{2}} + \sqrt{{0}^{2} + {6}^{2}}$

$p = \sqrt{64 + 36} + \sqrt{64 + 0} + \sqrt{0 + 36}$

$p = \sqrt{100} + \sqrt{64} + \sqrt{36}$

$p = 10 + 8 + 6$

$p = 24$