# What is the distance between (3, 9)  and (5, –3)?

Jan 22, 2016

To solve problems such as this one, you should use the distance formula (pythagorean theorem).

#### Explanation:

First, find the vertical and horizontal distances between the points.

Vertical distance = 9 + 3 = 12

Horizontal distance = |3 - 5| = |-2| = 2

So, assuming that the direct distance is the hypotenuse of our right triangle that has a horizontal length of 2 and a vertical height of 12, we now have enough information to do pythagorean theorem.

${a}^{2}$ + ${b}^{2}$ = ${c}^{2}$

${2}^{2}$ + ${12}^{2}$ = ${c}^{2}$

4 + 144 = ${c}^{2}$

√148 or 2√37 = c

So, the answer in exact form is 2√37 units and in decimal form is 12.17.

Here is a practice exercise:

Find the distance between (2, -4) and (-6 , 8)

Hopefully you understand now!