1. **State the problem:** We are given a rhombus STUV with points S(-1,4) and T(6,4). We need to find the length of side TU. 2. **Recall properties of a rhombus:** All sides of a rhombus are equal in length. Therefore, $ST = TU = UV = VS$. 3. **Calculate length of ST:** Use the distance formula between points $S(x_1,y_1)$ and $T(x_2,y_2)$: $$ST = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Substitute $S(-1,4)$ and $T(6,4)$: $$ST = \sqrt{(6 - (-1))^2 + (4 - 4)^2} = \sqrt{(6 + 1)^2 + 0^2} = \sqrt{7^2} = 7$$ 4. **Use rhombus property:** Since all sides are equal, $$TU = ST = 7$$ **Final answer:** $$TU = 7$$