Final answer:
To find the distance from the midpoint of a line segment with endpoints A(-1, 8) and B(5, 6) to the origin, calculate the midpoint's coordinates, then apply the distance formula to find it is approximately 7.28 units.
Step-by-step explanation:
The question asks for the distance from the midpoint of a line segment with endpoints A(-1, 8) and B(5, 6) to the origin (0, 0) on the Cartesian plane. To find the midpoint M, we average the x-coordinates and the y-coordinates of A and B separately. The midpoint M's coordinates are ((-1 + 5)/2, (8 + 6)/2) = (2, 7). Next, we find the distance between this midpoint M and the origin using the distance formula, √((x2 - x1)² + (y2 - y1)²). Plugging in the values, we get the distance = √((2 - 0)² + (7 - 0)²) = √(4 + 49) = √53, which is approximately 7.28 units.