Point P is the midpoint of the segment PQ. If P has coordinates (-3, 1) and Q has coordinates (7, 5), what are the coordinates of the other endpoint?

We are given $M(-3, 1)$ and $Q(7, 5)$. Let $P(x_P, y_P)$.
For the x-coordinate:

$$-3 = \frac{x_P + 7}{2}$$

For the y-coordinate:

$$1 = \frac{y_P + 5}{2}$$

Multiply both sides by 2:

$$-3 \times 2 = x_P + 7$$ $$-6 = x_P + 7$$

Subtract 7 from both sides:

$$x_P = -6 - 7$$ $$x_P = -13$$

Multiply both sides by 2:

$$1 \times 2 = y_P + 5$$ $$2 = y_P + 5$$

Subtract 5 from both sides:

$$y_P = 2 - 5$$ $$y_P = -3$$

The coordinates of P are $(-13, -3)$.

$$P(-13, -3)$$