Find the equation of the perpendicular bisector of the line segment whose end points are A(10, 4) and B( - 4, 9).

Perpendicular bisector: A perpendicular bisector is a line segment which is perpendicular to the given line segment and passes through its mid - point (or we can say bisects the line segment).

Now to find the equation of perpendicular bisector first, we will find mid - point of the given line using mid - point formula (call it midpoint as M),




Now we will calculate the slope of the given line and since lines are perpendicular, so the slope of two is related as m1.m2 = - 1.



Now the slope of perpendicular bisector is




Now equation of perpendicular bisector using two point form,




10y - 65 = 28x - 84


28x - 10y - 84 + 65 = 0


28x - 10y - 19 = 0


So, required equation of perpendicular bisector 28x - 10y - 19 = 0.


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