The equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8
Equation of a line
The equation of a line in slope intercept form is expressed as;
y = mx + b
The equation of the perpendicular bisector will be given as y = -1/m x+ b
where
m is the slope
b is the y-intercept
Determine the slope
Slope = -1-5/9-3
Slope = -6/6
Slope = -1
For the y-intercept
-1 = -1(9) + b
-1 = -9 + b
b = 8
Determine the equation
y = -1/m x + b
y = -1/(-1) x + 8
y = x + 8
Hence the equation of the perpendicular bisector of the segment with the endpoints (3,5) and (9,−1) is y = x + 8
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