# What is the distance between (1, 4) and (-6, -7)?

Apr 16, 2018

$d = \sqrt{170}$

d= 13.04 units

#### Explanation:

To find the distance between points at $\left(1 , 4\right)$ and $\left(- 6 , - 7\right)$

we can use the distance formula

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

for the points given
${x}_{1} = 1$
${y}_{1} = 4$
${x}_{2} = - 6$
${y}_{2} = - 7$

plugging in the values we get
$d = \sqrt{{\left(- 7 - 4\right)}^{2} + {\left(- 6 - 1\right)}^{2}}$

simplifying the parenthesis
$d = \sqrt{{\left(- 11\right)}^{2} + {\left(- 7\right)}^{2}}$

Simplifying the squares
$d = \sqrt{121 + 49}$

$d = \sqrt{170}$