# What is the distance between (3,5) and (0,6)?

Nov 30, 2015

distance = $\sqrt{10}$ or about $3.16227766017$

#### Explanation:

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

In this case,
$\left({x}_{1} , {y}_{1}\right) = \left(3 , 5\right)$
which means that ${x}_{1} = 3$ and ${y}_{1} = 5$
and
$\left({x}_{2} , {y}_{2}\right) = \left(0 , 6\right)$
which means that ${x}_{2} = 0$ and ${y}_{2} = 6$

If we plug this into the equation, we would get:
$d = \sqrt{{\left(0 - 3\right)}^{2} + {\left(6 - 5\right)}^{2}}$

we can simplify this into
$d = \sqrt{{\left(- 3\right)}^{2} + {\left(1\right)}^{2}}$
$d = \sqrt{9 + 1}$
$d = \sqrt{10}$

Therefore your distance (answer) would be $\sqrt{10}$ or about $3.16227766017$