1. **State the problem:** We need to plot and label points A, B, C, and D given in polar coordinates on a polar coordinate grid. 2. **Recall polar coordinates:** A point in polar coordinates is given as $(r, \theta)$ where $r$ is the radius (distance from origin) and $\theta$ is the angle measured from the positive polar axis (usually the positive x-axis). 3. **Important rule:** If $r$ is negative, the point is plotted by moving $|r|$ units in the direction opposite to the angle $\theta$. 4. **Plot each point:** - Point A: $(2, -\frac{\pi}{6})$ means move 2 units at angle $-\frac{\pi}{6}$ (which is $-30^\circ$). This is 2 units clockwise from the positive x-axis. - Point B: $(-3, -\frac{\pi}{2})$ means move 3 units opposite the angle $-\frac{\pi}{2}$ (which is $-90^\circ$). The opposite direction is $-\frac{\pi}{2} + \pi = \frac{\pi}{2}$ (or $90^\circ$), so plot 3 units at $90^\circ$. - Point C: $(-2, \frac{3\pi}{4})$ means move 2 units opposite the angle $\frac{3\pi}{4}$ (which is $135^\circ$). The opposite direction is $\frac{3\pi}{4} - \pi = -\frac{\pi}{4}$ (or $-45^\circ$), so plot 2 units at $-45^\circ$. - Point D: $(-2, -\frac{2\pi}{3})$ means move 2 units opposite the angle $-\frac{2\pi}{3}$ (which is $-120^\circ$). The opposite direction is $-\frac{2\pi}{3} + \pi = \frac{\pi}{3}$ (or $60^\circ$), so plot 2 units at $60^\circ$. 5. **Summary of final positions:** - A at radius 2, angle $-\frac{\pi}{6}$ - B at radius 3, angle $\frac{\pi}{2}$ - C at radius 2, angle $-\frac{\pi}{4}$ - D at radius 2, angle $\frac{\pi}{3}$ 6. **Label each point accordingly on the polar grid.**