# What is the distance between the origin of a Cartesian coordinate system and the point (5, -2)?

Apr 8, 2015

$= \sqrt{29}$

#### Explanation:

The origin is $\left({x}_{1} , {y}_{1}\right) = \left(0 , 0\right)$
and our second point is at $\left({x}_{2} , {y}_{2}\right) = \left(5 , - 2\right)$

The horizontal distance (parallel to the x-axis) between the two points is 5
and
the vertical distance (parallel to the y-axis) between the two points is 2.

By the Pythagorean Theorem the distance between the two points is
$\sqrt{{5}^{2} + {2}^{2}}$

$= \sqrt{29}$