Answer
IV
Work Step by Step
To plot the point $(r, \theta )=(-4, 135^{\circ })$, begin with the $135^{\circ }$ angle. Because $135^{\circ }$ is a positive angle, draw $\theta = 135^{\circ }$ counterclockwise from the polar axis. Now consider $r=-4$. Because $r \lt 0$, plot the point by going out four units along the ray opposite the terminal side of $\theta$.
So, looking at the graph, we see that the point lies in the quadrant IV.
