# How do we find the distance between (-4.5,-4.5) and (3.5,3.5)?

Aug 31, 2016

Distance between $\left(- 4.5 , - 4.5\right)$ and $\left(3.5 , 3.5\right)$ is $8 \sqrt{2}$

#### Explanation:

The distance. Between two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ is given by

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

Hence distance between $\left(- 4.5 , - 4.5\right)$ and $\left(3.5 , 3.5\right)$ is given by

$\sqrt{{\left(3.5 - \left(- 4.5\right)\right)}^{2} + {\left(3.5 - \left(- 4.5\right)\right)}^{2}}$

= $\sqrt{{8}^{2} + {8}^{2}}$

= $\sqrt{64 + 64}$

= sqrt128=sqrt(8^2×2)

= $8 \sqrt{2}$