1. **State the problem:** We have a parallelogram ABCD with points A(0,0), B(2,4), and C(10,4). We need to find the coordinates of point D. 2. **Formula and rule:** 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. **Calculate midpoint of AC:** $$\text{Midpoint}_{AC} = \left(\frac{0+10}{2}, \frac{0+4}{2}\right) = (5, 2)$$ 4. **Let D be (x,y). Calculate midpoint of BD:** $$\text{Midpoint}_{BD} = \left(\frac{2+x}{2}, \frac{4+y}{2}\right)$$ 5. **Set midpoints equal:** $$\left(\frac{2+x}{2}, \frac{4+y}{2}\right) = (5, 2)$$ 6. **Solve for x and y:** $$\frac{2+x}{2} = 5 \implies 2+x = 10 \implies x = 8$$ $$\frac{4+y}{2} = 2 \implies 4+y = 4 \implies y = 0$$ 7. **Conclusion:** The coordinates of D are $(8, 0)$. **Final answer:** $(8, 0)$