Final answer:
The segment with endpoints A(-4,2) and B(5,10) has a length of approximately 12.04 units. The midpoint of the segment is located at coordinates (0.5, 6).
Step-by-step explanation:
Finding the Length of a Segment and Coordinates of Its Midpoint
To find the length of the segment with endpoints A(-4,2) and B(5,10), we use the distance formula which is derived from the Pythagorean theorem:
Distance = √[(x2-x1)² + (y2-y1)²].
In this case, x1 = -4, y1 = 2, x2 = 5, and y2 = 10. Plugging these into the formula, we get:
Distance = √[(5 - (-4))² + (10 - 2)²] = √[(5 + 4)² + (8)²] = √[9² + 8²] = √[81 + 64] = √145 ≈ 12.04 units.
The midpoint of a segment is the average of the x-coordinates and the y-coordinates of the endpoints, which can be found using the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
Applying the midpoint formula to our endpoints we find:
Midpoint = ((-4 + 5)/2, (2 + 10)/2) = (1/2, 12/2) = (0.5, 6).
The length of the segment AB is approximately 12.04 units, and the midpoint coordinates are (0.5, 6).