What is the distance between (31,-21) and (21,-29)?

Dec 16, 2015

$2 \sqrt{41}$ units

Explanation:

The distance between two points can be calculated with the formula:

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

where:
$d =$distance
$\left({x}_{1} , {y}_{1}\right) = \left(31 , - 21\right)$
$\left({x}_{2} , {y}_{2}\right) = \left(21 , - 29\right)$

Substitute your known values into the distance formula to find the distance between the two points:

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$
$d = \sqrt{{\left(\left(21\right) - \left(31\right)\right)}^{2} + {\left(\left(- 29\right) - \left(- 21\right)\right)}^{2}}$
$d = \sqrt{{\left(- 10\right)}^{2} + {\left(- 8\right)}^{2}}$
$d = \sqrt{100 + 64}$
$d = \sqrt{164}$
$d = 2 \sqrt{41}$

$\therefore$, the distance between the two points is $2 \sqrt{41}$ units.