# How do use the pythagorean theorem to find the distance between two points like the points (1,3) and (4,3)?

Mar 2, 2016

The distance between the points is 3

#### Explanation:

Let the distance between points be $d$ then

Let $\left({x}_{1} , {y}_{1}\right) \to \left(1 , 3\right)$
Let $\left({x}_{2} , {y}_{2}\right) \to \left(4 , 3\right)$

Then by Pythagoras

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

${d}^{2} = {\left(4 - 1\right)}^{2} + {\left(3 - 3\right)}^{2}$

Notice that ${y}_{1} = {y}_{2}$ which means that the line between the points is parallel to the x-axis as there is no change in height (y-axis).

$\textcolor{b r o w n}{\text{However, the Pythagoras theorem will still work}}$

${d}^{2} = {3}^{2} + {0}^{2}$

$\sqrt{{d}^{2}} = \sqrt{{3}^{2}}$

$d = 3$