Final answer:
The perpendicular bisector of the line segment with endpoints (-2, 4) and (1, 5) must go through their midpoint, which is calculated to be at (-0.5, 4.5).
Step-by-step explanation:
The point through which the perpendicular bisector of the segment with endpoints (-2, 4) and (1, 5) must pass can be found by first calculating the midpoint of the two points and then using the point-slope form to determine the equation of the bisector. The midpoint (M) can be calculated using the formula for the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) as follows:
M = ((x1 + x2)/2, (y1 + y2)/2)
Substitute the given points into the formula:
M = ((-2 + 1)/2, (4 + 5)/2)
M = (-0.5, 4.5)
Thus, the midpoint is at (-0.5, 4.5). Since the perpendicular bisector passes through the midpoint of the line segment, it must go through the point (-0.5, 4.5).