1. **Problem statement:** Given points $A(2,3)$ and $B(-1,-4)$, find the distance $|AB|$. 2. **Formula for distance between two points:** $$|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where $A = (x_1, y_1)$ and $B = (x_2, y_2)$. 3. **Substitute values:** $$|AB| = \sqrt{(-1 - 2)^2 + (-4 - 3)^2} = \sqrt{(-3)^2 + (-7)^2}$$ 4. **Calculate squares:** $$|AB| = \sqrt{9 + 49} = \sqrt{58}$$ 5. **Final answer:** $$|AB| = \sqrt{58} \approx 7.6158$$ This is the length of the line segment $AB$.