# What is the distance between (8,5) and (1,2)?

Jan 3, 2016

$\text{distance} = \sqrt{58}$

#### Explanation:

We can find this distance using Pythagoras' formula. But now we only have one side of the triangle, so, we need to complete the rectangle triangle, and in order to make a $\frac{\pi}{2}$ angle, we have to create two lines, one with the projection of the extremes in $x$ axis, and the other with the projections in $y$ axis. Then, we take the difference between the lines of both projections:
$\triangle x = 8 - 1 = 7$
$\triangle y = 5 - 2 = 3$

Now, apply the formula: ${\text{distance}}^{2} = {7}^{2} + {3}^{2}$
$\text{distance} = \sqrt{58}$