Answer:
To solve this problem, we need to take the following steps:
Step 1: Calculate the midpoint by adding the x-values together and dividing by 2 and the y-values together and dividing by 2.
Step 2: The midpoint of the segment is (4, -1).
Step 3: Calculate the slope of the perpendicular bisector by taking the opposite reciprocal of the original segment’s slope.
Step 4: The original segment’s slope is -2, so the perpendicular bisector’s slope is 1/2.
Step 5: Use point-slope form to write the equation of the perpendicular bisector with (4, -1) as the given point and 1/2 as the given slope. The equation is y + 1 = 1/2(x - 4).
Therefore, the equation of the perpendicular bisector that goes through a segment with endpoints (2,1) and (6, -3) is y + 1 = 1/2(x - 4).