Final answer:
To find the equation of the perpendicular bisector, determine the midpoint and slope of the line segment. Then, use the midpoint and negative reciprocal of the slope to write the equation of the perpendicular bisector.
Step-by-step explanation:
To find the equation of the perpendicular bisector, we need to determine the midpoint of the line segment and its slope. First, we find the midpoint by averaging the x-coordinates and the y-coordinates of the endpoints: ((1+(-7))/2, (3+7)/2) = (-3,5).
Next, we find the slope of the line segment using the slope formula: slope = (7-3)/(-7-1) = 4/(-8) = -1/2.
Finally, we use the midpoint and the negative reciprocal of the slope to write the equation of the perpendicular bisector. The equation is y - 5 = (-1/2)(x + 3), or y = (-1/2)x + 7.5.