Question

The point A has co-ordinates (-1,6) and the point B has coordinates (7,2).
Find the equation of the perpendicular bisector of AB. give your answer in the form y=mx+c
A point C on the perpendicular bisector has coordinates (p,q). the Distance OC is 2 units where O is the origin. write down the distance OC is 2 units, where O is the origin. write down two equations involving p and q and hence find the coordinates of the possible positions of C

Answer 1

x1+x2/2,y1+y2/2)=(3,4)
m of perp bisector=2
y=mx+c
4=2(3)+c
c=-2
y=2x-2
q=2p-2
O(0,0) C(p,q)
((x2-x1)^2+(y2-y1)^2)^1/2=length between two points
((p-0)^2+(q-0)^2)^1/2=2
(p^2+q^2)=4
p^2+(2p-2)^2=4
p^2+(2p-2)(2p-2)=4
p^2+4p^2-4p-4p+4=4
5p^2-8p=0
p(5p-8)
p=0 or 8/5
q=2p-2
plug p=0
q=-2
plug p=8/5
q=2*8/5-2
q=1.2