Answer
III
Work Step by Step
To plot the point $(r, \theta )=(-3, \frac{\pi }{4})$, begin with the $\frac{\pi }{4}$ angle. Because $\frac{\pi }{4}$ is a positive angle, draw $\theta = \frac{\pi }{4}$ counterclockwise from the polar axis. Now consider $r=-3$. Because $r \lt 0$, plot the point by going out three units along the ray opposite the terminal side of $\theta$.
So, looking at the graph, we see that the point lies in the quadrant III.
