Final answer:
The midpoint of the line segment with endpoints (2,4) and (-4,-1) is (-1,1.5), and the distance between these two points is approximately 7.07 units.
Step-by-step explanation:
To find the midpoint, we use the Midpoint Formula, which states that the coordinates of the midpoint (M) between two points (x1, y1) and (x2, y2) are given by ( (x1 + x2)/2, (y1 + y2)/2 ). Applying this formula to the given endpoints (2,4) and (-4,-1), we calculate (-1,1.5) as the midpoint.
Next, we determine the distance between the two points using the Distance Formula, which is expressed as √((x2 - x1)² + (y2 - y1)²). Plugging in the coordinates, we obtain √((-4 - 2)² + (-1 - 4)^2) = √((-6)² + (-5)²) = √(36 + 25) = √61. Thus, the distance between (2,4) and (-4,-1) is approximately 7.07 units.
In summary, the midpoint is (-1,1.5), and the distance between the given points is approximately 7.07 units.