# How do you find the distance between P(-5, -4) and P(7, 5)?

Sep 17, 2017

Use Pythagoras' Theorem 😃

#### Explanation:

Imagine that the distance between two points is the hypotenuse of a triangle. We need to find the base and the height of the triangle to get the hypotenuse.

First, find the distance between the x-coordinates. You find the distance between the two x-coordinates along the same y-coordinate. This is found by counting the distance from 0 to another point and adding those together.

-5 to get to 0 takes 5 units.
0 to 7 takes 7 units.
7+5=12 units

Where the distance ends is (7,-4) because the original coordinate was (-5, -4).

Second, do the same now but for the y-coordinates. From (7,-4) count how many units it takes to get to (7, 5).

From -4 to 0 takes 4 units.
0 to 5 takes 5 units.
4+5 = 9 units.

Now that we have the base and height, we use Pythagoras' Theorem to find the distance:
${12}^{2} + {9}^{2} = {c}^{2}$
${c}^{2} = 225$
$c = 15$

Hope this helps!