# How do you find the distance between points (-5,2), (4,-2)?

May 28, 2018

The distance is $\sqrt{97}$ or $\approx 9.85$

#### Explanation:

The distance between two points is shown by the formula:
$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

We have the values for the two coordinates, so we can substitute them into the distance formula:
$d = \sqrt{{\left(- 2 - 2\right)}^{2} + {\left(4 - \left(- 5\right)\right)}^{2}}$

And now we simplify:
$d = \sqrt{{\left(- 4\right)}^{2} + {\left(9\right)}^{2}}$

$d = \sqrt{16 + 81}$

$d = \sqrt{97}$

If you want the exact distance, you can leave it as $\sqrt{97}$, but if you want it in decimal form, it is $\approx 9.85$ (rounded to nearest hundredth's place).

Hope this helps!