Question

The line segment joining A[-1,5/3] and B (a,5) is divided in the ratio 1:3 at P,the point where the line segment AB intersects y-axis. Find
1. The value of a
2. The coordinates of P.

Answer 1

if point p is at y axis so coordinate of p is (0,y).
so by section formula,
(0,y)=(a-3/4,5+5/3*3)
(0,y)=(a-3/4,5+5/4)
so,
a-3/4=0
so, a=3
and y=5+5/4
=5/2
so coordinate of p=(0,5/2)