1. **State the problem:** We are given a rectangle DEFG with center C at coordinates $C(7,9)$ and one vertex $E(20,26)$. We need to find the coordinates of vertex $G$. 2. **Recall the property of the center of a rectangle:** The center $C$ is the midpoint of the diagonal connecting opposite vertices. Since $C$ is the midpoint of diagonal $EG$, the coordinates of $C$ are the average of the coordinates of $E$ and $G$. 3. **Use the midpoint formula:** $$C = \left(\frac{x_E + x_G}{2}, \frac{y_E + y_G}{2}\right)$$ Given $C(7,9)$ and $E(20,26)$, we have: $$7 = \frac{20 + x_G}{2}$$ $$9 = \frac{26 + y_G}{2}$$ 4. **Solve for $x_G$:** Multiply both sides by 2: $$2 \times 7 = 20 + x_G$$ $$14 = 20 + x_G$$ Subtract 20 from both sides: $$14 - 20 = x_G$$ $$x_G = -6$$ 5. **Solve for $y_G$:** Multiply both sides by 2: $$2 \times 9 = 26 + y_G$$ $$18 = 26 + y_G$$ Subtract 26 from both sides: $$18 - 26 = y_G$$ $$y_G = -8$$ 6. **Final answer:** The coordinates of $G$ are $(-6, -8)$.