# How do you find the distance between (7,2), (-5,7)?

Mar 30, 2018

$13$

#### Explanation:

The easiest way to find the distance between two points is to use the distance formula:
d = sqrt((x_2 - x_1)^2 + (y_2-y_1)^2

It looks really complicated and confusing, but I'll help you through it.

Remember that points are in the form: $\left(x , y\right)$.

• I am going to call $\left(7 , 2\right)$ Point 1, so:
${x}_{1} = 7$
${y}_{1} = 2$
• I'm going to call $\left(- 5 , 7\right)$ Point 2, so:
${x}_{2} = - 5$
${y}_{2} = 7$

Now all we have to do is substitute those into the equation and solve. Here goes nothing:

d = sqrt((x_2 - x_1)^2 + (y_2-y_1)^2

d = sqrt((-5 - 7)^2 + (7-2)^2

d = sqrt((-12)^2 + (5)^2

d = sqrt(144 + 25

$d = \sqrt{169}$

$d = 13$

So the distance between $\left(7 , 2\right)$ and $\left(- 5 , 7\right)$ is $13$.