Question

find the coordinate of a point p on the line segment joining A(3,-3) and B(6,7) such that Ap=2/5 AB

Answer 1

5 AP = 2 AB
5/2 = AB/AP
5/2 - 1 = AB/AP - 1
3/2 = PB/AP
AP/PB = 2/3
Point P divides the line in the ratio 2:3
Applying section formula
x = (12 + 9)/ 2+3 = 21/5
y = (14 - 9)/ 2+3 = 5/5 = 1
So the coordinates of point P are
( 21/5 , 1 )