**Step 1 — Understand trisection.**
Points $P$ and $Q$ trisect $AB$, so
$$AP : PB = 1 : 2 \qquad\text{and}\qquad AQ : QB = 2 : 1$$

**Step 2 — Recall the section formula.**
$$\left(\frac{m x_2 + n x_1}{m+n},\ \frac{m y_2 + n y_1}{m+n}\right)$$

**Step 3 — Find P (ratio 1 : 2).**
$$P = \left(\frac{1(-3) + 2(-1)}{1+2},\ \frac{1(-2) + 2(4)}{1+2}\right)$$
$$= \left(\frac{-3-2}{3},\ \frac{-2+8}{3}\right) = \left(\frac{-5}{3},\ \frac{6}{3}\right) = \left(-\frac53,\ 2\right)$$

**Step 4 — Find Q (ratio 2 : 1).**
$$Q = \left(\frac{2(-3) + 1(-1)}{2+1},\ \frac{2(-2) + 1(4)}{2+1}\right)$$
$$= \left(\frac{-6-1}{3},\ \frac{-4+4}{3}\right) = \left(-\frac73,\ 0\right)$$

**Step 5 — Final answer.**
$$\boxed{P\left(-\frac53,\ 2\right) \quad \text{and} \quad Q\left(-\frac73,\ 0\right)}$$