1. **Stating the problem:** We have a square ABCD with vertices A(3,7), B(3,3), and D(7,7). We need to find the coordinates of the fourth vertex C. 2. **Formula and rules:** In a square, all sides are equal and adjacent sides are perpendicular. The coordinates of the fourth vertex can be found using vector addition: $$\vec{C} = \vec{B} + \vec{D} - \vec{A}$$ 3. **Calculate vectors:** - $\vec{A} = (3,7)$ - $\vec{B} = (3,3)$ - $\vec{D} = (7,7)$ 4. **Apply the formula:** $$\vec{C} = (3,3) + (7,7) - (3,7) = (3+7-3, 3+7-7) = (7,3)$$ 5. **Interpretation:** The coordinates of point C are (7,3). 6. **Check options:** Option B is C(7,3), which matches our calculation. **Final answer:** The coordinates of point C are **(7,3)**.