Final answer:
The length of the line segment joining points A(2,5) and B(-3,-6) is calculated with the distance formula, yielding approximately 12.08 units.
Step-by-step explanation:
To find the length of the line segment joining the points A(2,5) and B(-3,-6), we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is given by:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates of points A and B:
Distance = √[(-3 - 2)^2 + (-6 - 5)^2]
Distance = √[(-5)^2 + (-11)^2]
Distance = √[25 + 121]
Distance = √[146]
Distance ≈ 12.08 units
Therefore, the length of the line segment is approximately 12.08 units. This calculation utilizes the Cartesian coordinate system to measure the distance between two points analytically.