Answer
$r = \sqrt{13}$
Work Step by Step
The terminal side of $\theta$ in its standard position is represented by the blue line in the figure.
To find the distance from the origin to $(2,-3)$, we use the distance formula
$$r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r=\sqrt{(2-0)^2+(-3-0)^2}=\sqrt{13}$$
