Question

Point P lies on the directed line

segment from A(-2, 4) to B(7, -2), and
partitions the segment in the ratio 1 to 2.
Find the coordinates of P

Answer 1

Explanation:

The vector AP is in the same directionas AB but its length is 1/3 of AB

No AB = (7-(-2)) i + (-2-4)j = 9i -6j.

It follows that AP = (1/3)(9i-6j) = 3i - 2j.

Now OP = OA +AP = (-2i + 4 j ) + (3i-2j) = i + 2j

So P(1,2).