1. **State the problem:** We have a square ABCD with points A at (3, 4) and D at (10, 4). We need to find the coordinates of point C. 2. **Analyze given points:** Points A and D lie on the same horizontal line since their y-coordinates are both 4. 3. **Calculate side length:** The length of side AD is the distance between A and D along the x-axis: $$AD = 10 - 3 = 7$$ 4. **Properties of a square:** All sides are equal and adjacent sides are perpendicular. 5. **Find coordinates of B and C:** Since AD is horizontal, sides AB and DC are vertical lines of length 7. 6. **Coordinates of B:** Point B is directly above A by 7 units: $$B = (3, 4 + 7) = (3, 11)$$ 7. **Coordinates of C:** Point C is directly above D by 7 units: $$C = (10, 4 + 7) = (10, 11)$$ **Final answer:** The coordinates of point C are $\boxed{(10, 11)}$.