Final answer:
The equation of the perpendicular bisector of the segment with endpoints A(-1, -1) and B(5, 3) is y = (-3/2)x + 4.
Step-by-step explanation:
To find the equation of the perpendicular bisector of the segment with endpoints A(-1, -1) and B(5, 3), we first find the midpoint of the segment. The midpoint is ((-1 + 5)/2, (-1 + 3)/2) = (2, 1).
Now we find the slope of AB, which is (3 - (-1))/(5 - (-1)) = 4/6 = 2/3. Since the slope of the perpendicular bisector is the negative reciprocal of the slope of AB, the slope of the perpendicular bisector is -3/2.
Finally, we use the point-slope form of a line with the midpoint and the slope to find the equation of the perpendicular bisector: y - 1 = (-3/2)(x - 2), or y = (-3/2)x + 4.