Answer
II
Work Step by Step
To plot the point $(r, \theta )=(-2, -\frac{\pi }{4})$, begin with the $-\frac{\pi }{4}$ angle. Because $-\frac{\pi }{4}$ is a negative angle, draw $\theta = -\frac{\pi }{4}$ clockwise from the polar axis. Now consider $r=-2$. Because $r \lt 0$, plot the point by going out two units along the ray opposite the terminal side of $\theta$.
So, looking at the graph, we see that the point lies in the quadrant II.
