# What is the distance of (–4, 7) and (–7, 8)?

Jun 15, 2017

$D \left(A , B\right) = \sqrt{10} \approx 3.1623$

#### Explanation:

The distance between two points $A = \left({x}_{1} , {y}_{1}\right)$ and $B = \left({x}_{2} , {y}_{2}\right)$ is given by the distance formula.

$D \left(A , B\right) = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

We are given

$\left({x}_{1} , {y}_{1}\right) = \left(- 4 , 7\right)$

and

$\left({x}_{2} , {y}_{2}\right) = \left(- 7 , 8\right)$

Plugging these values into the distance formula gives:

$D \left(A , B\right) = \sqrt{{\left(- 7 - \left(- 4\right)\right)}^{2} + {\left(8 - 7\right)}^{2}}$

$D \left(A , B\right) = \sqrt{{\left(- 7 + 4\right)}^{2} + {\left(8 - 7\right)}^{2}}$

$D \left(A , B\right) = \sqrt{{\left(- 3\right)}^{2} + {\left(1\right)}^{2}}$

$D \left(A , B\right) = \sqrt{9 + 1}$

$D \left(A , B\right) = \sqrt{10} \approx 3.1623$