Question

Find the equation of the perpendicular bisector of the line segment joining the points (1,1) and (2,4).

Answer 1

A(1,1) , B(2,3)

The point that bisect the line AB

P = {(1+2)/2 , (1+3)/2}

P {(3/2),2}

The equation of line perpendicular to AB and passing through point P is ;

slope of AB =

m = 2

m'×2 = -1

m' = -1/2

equation of line

1x+ 2y +k =0

passes through point P

(3/2)+(2×2)+k = 0

(3/2) + 4 + k = 0

k = -11/2

the equation of the line is

x+2y-11/2 = 0

2x+4y-11 = 0