Final answer:
By determining endpoint B using the midpoint formula and then applying the distance formula, we find that the length of segment AB is approximately 30.5 units to the nearest tenth.
Step-by-step explanation:
To find the length of segment AB given the endpoint A (-5,12) and midpoint (9,6), we first need to determine the coordinates of the endpoint B.
Since the given point is the midpoint, its coordinates are the average of the coordinates of points A and B. From the midpoint formula:
(x1 + x2) / 2 = xm, and (y1 + y2) / 2 = ym
We have:
(-5 + xB) / 2 = 9, and (12 + yB) / 2 = 6
By solving these equations, we get the coordinates of B as (23, 0).
To find the straight-line distance between points A and B, we use the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2]
Substituting the coordinates, we have:
d = √[(23 - (-5))2 + (0 - 12)2] = √(282 + 122) = √(784 + 144) = √928 ≈ 30.5
The length of segment AB is approximately 30.5 units to the nearest tenth.