Question

The point P divides the line segment joining the points A and B with coordinates (1, 2) and (3, −4) respectively into two parts such that 2AB = 3BP. Find the coordinates of P. In this question of subjective test why is it written AP:BP=1:2 and not 3:2

Answer 1

let p (x, y)
a/c 2AB=3BP
squaring both side
4AB^2=9BP^2
4 {(2)^2+(-6)^2}=9 {(3-x)^2+(y+4)^2} -----(1)
now AP/BP=1/2
squaring both side
AP^2/BP^2=1/4
{(1-x)^2+(2-y)^2}/{(3-x)^2+(4+y)^2}=1/4 ---(2)
solve both equation find cordinate of P