1. **Problem:** Find the length and midpoint of the segment with endpoints (6,11) and (8,4). 2. **Formulas:** - Distance formula: $$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$ - Midpoint formula: $$M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$$ 3. **Calculate the length:** $$d=\sqrt{(8-6)^2+(4-11)^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}$$ 4. **Calculate the midpoint:** $$M=\left(\frac{6+8}{2},\frac{11+4}{2}\right)=\left(7,7.5\right)$$ 5. **Answer:** - Length of segment: $\sqrt{53}$ - Midpoint: $(7,7.5)$