Find the equation of the perpendicular bisector of AB where A and B are the points (3,6) and (-3,4) respectively. Also find its point of intersection with (i) x-axis and (ii) y-axis.
The perpendicular bisector of the line joining two given points is perpendicular to the line and passes through the mid point of the line.
Let A (3, 6) and B (-3, 4) be the two given points.
Mid-Point of AB= =(0,5)
Slope of AB=
Slope of the required line=-3
The equation of the required line
(y-5)=-3(x-0)
y-5=-3x
3x+y-5=0
Thus the required equation of the line is 3x+y-5=0
Now when it cuts x-axis then y=0 so,
3x+0-5=0
or x = 5/3 so point = (5/3,0)
when it cuts y-axis then x=0 so
0+y-5 = 0
y=5
so point = (0,5)