1. **Problem Statement:** Given a parallelogram ABCD with points A(-11, 23), B(-13, 29), and C(5, 22), find the coordinates of point D. 2. **Formula and Concept:** In a parallelogram, the diagonals bisect each other. This means the midpoint of diagonal AC is the same as the midpoint of diagonal BD. 3. **Midpoint Formula:** The midpoint M of a segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ 4. **Calculate Midpoint of AC:** $$M_{AC} = \left(\frac{-11 + 5}{2}, \frac{23 + 22}{2}\right) = \left(\frac{-6}{2}, \frac{45}{2}\right) = (-3, 22.5)$$ 5. **Let D = (x, y). Calculate Midpoint of BD:** $$M_{BD} = \left(\frac{-13 + x}{2}, \frac{29 + y}{2}\right)$$ 6. **Set Midpoints Equal:** Since $M_{AC} = M_{BD}$, $$\frac{-13 + x}{2} = -3 \quad \Rightarrow \quad -13 + x = -6 \quad \Rightarrow \quad x = 7$$ $$\frac{29 + y}{2} = 22.5 \quad \Rightarrow \quad 29 + y = 45 \quad \Rightarrow \quad y = 16$$ 7. **Answer:** The coordinates of point D are $(7, 16)$. This method uses the property of parallelograms that their diagonals bisect each other, allowing us to find the missing vertex by equating midpoints.