# What is the distance between the origin of a Cartesian coordinate system and the point (-6, 5)?

Oct 15, 2015

$\sqrt{61}$.
To reach the point $\left(- 6 , 5\right)$ starting from the origin, you must take $6$ steps to the left, and then $5$ upwards. This "walk" shows a right triangle, whose catheti are this horizontal and vertical line, and whose hypotenuse is the line connecting the origin to the point, which we want to measure.
But since the catheti are $6$ and $5$ units long, the hypotenuse must be
$\sqrt{{5}^{2} + {6}^{2}} = \sqrt{25 + 36} = \sqrt{61}$