Question

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 1) x axis and 2) y axis

Answer 1

I would help you with the approach and I hope you can do it on your own!

A perpendicular bisector of a given line segment is a line passing through the mid-point of the given line segment and is perpendicular to it.

For two given points (x1,y1x1,y1) and (x2,y2x2,y2), the mid-point is given by (h,k) = (x1+x22,y1+y22x1+x22,y1+y22)

Gradient of the line joining the two points (x1,y1x1,y1) and (x2,y2x2,y2) is given by m1 =y2−y1x2−x1m1 =y2−y1x2−x1

So, gradient of any line perpendicular to the line joining the two points (x1,y1x1,y1) and (x2,y2x2,y2) is m2 =−1m1m2 =−1m1


Therefore, the equation of the perpendicular bisector of A(x1,y1x1,y1) and B(x2,y2x2,y2) is:

y−k =m2(x−h)y−k =m2(x−h)

I hope it helps!

Answer 2

A and B are the points (3,6) and (-3,4)
let perpendicular bisector be Y=mx+c
midpoint ( 0,5)  so c=5
slope of AB 2/6
slope of perpendicular (m) = -3

equation y=-3x+5