1. **State the problem:** We are given a point $P(-2, -3)$ and need to find a second point that is 4 units away from $P$ and has an $x$-coordinate of $-2$. 2. **Formula used:** The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Apply the known values:** Here, $d = 4$, $x_1 = -2$, $y_1 = -3$, and $x_2 = -2$ (given). We need to find $y_2$. 4. **Set up the equation:** $$4 = \sqrt{(-2 - (-2))^2 + (y_2 - (-3))^2} = \sqrt{0 + (y_2 + 3)^2} = |y_2 + 3|$$ 5. **Solve for $y_2$:** $$|y_2 + 3| = 4$$ This gives two cases: - $y_2 + 3 = 4 \implies y_2 = 1$ - $y_2 + 3 = -4 \implies y_2 = -7$ 6. **Final answer:** The coordinates of the second point are: $$(-2, 1) \text{ or } (-2, -7)$$