Final answer:
The equation of the perpendicular bisector of segment AB with endpoints at (-2, 3) and (10, 7) is not provided in the options, but through calculation, the correct equation is found to be y = -3x + 17.
Step-by-step explanation:
To find the equation of the perpendicular bisector of segment AB with endpoints at (-2, 3) and (10, 7), we first calculate the midpoint of the segment and its slope. The slope of AB is (7 - 3) / (10 - (-2)) = 4 / 12 = 1/3. The midpoint is ((-2 + 10) / 2, (3 + 7) / 2) which simplifies to (4, 5).
Since the perpendicular bisector has to be perpendicular to AB, its slope is the negative reciprocal of 1/3, which is -3. Using the point-slope form of a line, y - y1 = m(x - x1), with the midpoint (4, 5) and the slope -3, we get:
y - 5 = -3(x - 4)
y - 5 = -3x + 12
Adding 5 to both sides gives us:
y = -3x + 17
Since none of the provided options match this equation, it may be that there's been an error either in the question or in the available answer choices.