Question

Let A and B be
two points in the plane, as shown in the figure.
(a) Prove that B
A
O
A  O
B, where O is the
origin.
(b) Let C be a point on the line segment BA
which divides the segment in the ratio x : y
where x  y
1. That is,
 

B
C

C

A





x
y
.
Show that O
C
= xO
A  + yO
B.