Find the distance between the two labeled points?

Mar 22, 2017

The distance is $| A B | = 5 \sqrt{2}$. See explanation

Explanation:

To find the distance between 2 points: $A = \left({x}_{A} , {y}_{A}\right)$ and $B = \left({x}_{B} , {y}_{B}\right)$ you use the formula:

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

If we use this formula for the given points we get:

$| A B | = \sqrt{{\left(2 - \left(- 3\right)\right)}^{2} + {\left(3 - \left(- 2\right)\right)}^{2}} = \sqrt{{\left(2 + 3\right)}^{2} + {\left(3 + 2\right)}^{2}} =$

$= \sqrt{{5}^{2} + {5}^{2}} = \sqrt{50} = 5 \sqrt{2}$