Answer:
x -2y = 0
Step-by-step explanation:
A perpendicular bisector is a line perpendicular to a given line or segment that goes through the midpoint between given points. The perpendicular line will have a slope that is the opposite reciprocal of the slope of the segment between the given points.
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The midpoint between A and B is ...
M = (A +B)/2
M = ((5, 5) +(7, 1))/2 = (12, 6)/2 = (6, 3)
The slope of the line between A and B is ...
m = (y2 -y1)/(x2 -x1)
m = (1 -5)/(7 -5) = -4/2 = -2
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The opposite reciprocal of the slope of the given segment is ...
m' = -1/-2 = 1/2
The point-slope form of the equation of the perpendicular bisector can be written as ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -3 = 1/2(x -6) . . . . line with slope 1/2 through point (6, 3)
Multiplying by 2 gives ...
2y -6 = x -6
Subtracting (2y -6) gives the standard-form equation ...
x -2y = 0
