Final answer:
The point on the perpendicular bisector of the segment with endpoints (-2,5) and (-2,-3) can have any x-coordinate and a y-coordinate of 1/2.
Step-by-step explanation:
The perpendicular bisector of a line segment is a line that divides the segment into two equal halves and is perpendicular to the segment. To find the equation of the perpendicular bisector of the segment with endpoints (-2,5) and (-2,-3), we need to find the midpoint of the segment first. The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints. In this case, the x-coordinate of both endpoints is -2, so the average is also -2. The y-coordinate of the midpoint is (5 + -3)/2 = 1/2. Therefore, the midpoint is (-2, 1/2).
Since the perpendicular bisector passes through the midpoint and is perpendicular to the segment, its slope is the negative reciprocal of the slope of the segment. The slope of the segment is undefined because both endpoints have the same x-coordinate. Therefore, the slope of the perpendicular bisector is 0. Using the point-slope form of a line, the equation of the perpendicular bisector is y - 1/2 = 0(x + 2), which simplifies to y = 1/2.
Therefore, the point on the perpendicular bisector is any point with a y-coordinate of 1/2, and its x-coordinate can be any real number.