1. **State the problem:** Find the distance $d$ between points $A=(11,-5)$ and $B=(1,7)$ on the coordinate plane. 2. **Formula:** The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$d=\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ This formula comes from the Pythagorean theorem, treating the difference in $x$ and $y$ as legs of a right triangle. 3. **Substitute values:** $$d=\sqrt{(1 - 11)^2 + (7 - (-5))^2}$$ 4. **Simplify inside the square root:** $$d=\sqrt{(-10)^2 + (12)^2}$$ $$d=\sqrt{100 + 144}$$ 5. **Add inside the root:** $$d=\sqrt{244}$$ 6. **Calculate the square root:** $$d=\sqrt{4 \times 61} = \sqrt{4} \times \sqrt{61} = 2\sqrt{61}$$ 7. **Approximate the decimal value:** $$d \approx 2 \times 7.8102 = 15.6204$$ 8. **Round to the nearest tenth:** $$d \approx 15.6$$ **Final answer:** The distance between points $A$ and $B$ is approximately $15.6$ units.