Final answer:
To calculate the length of AB, we use the distance formula and substitute the coordinates, resulting in AB being 10 units long, which is not listed in the provided options.
Step-by-step explanation:
To find the length of segment AB with endpoints A(-4, 1) and B(2, -7), we use the distance formula which is derived from the Pythagorean theorem. The formula is as follows:
AB = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the given coordinates:
AB = √[(2 + 4)^2 + (-7 - 1)^2]
AB = √[6^2 + (-8)^2]
AB = √[36 + 64]
AB = √[100]
AB = 10
The correct answer for part (b) is that the length of AB is not 65, 74, 85, or 90, but it is 10, which is not included in the options provided.