Question

Point P divides the line segment joining the points A(-1,3) and B(9,8) such that AP/PB=k/1. If P lies on line x-y+2=0 , find the value of k.

Answer 1

Simply find coordinates of point P
by this method Internal division of a line segment:

Consider the point P(x_P , y_P) that lies on the line segment AB joining points A(x_A , y_B) and B(x_A , y_B):

Point P divides AB in the ratio k₁ : k₂ , and the coordinates of point P are given by these formulas:

The blue formula is for three dimensional space, where you have 'z' coordinates as well as 'x' and 'y'.

When point P lies between points A and B, it divides AB internally.

it is given that the line segment joining A{-1,3} and B{9,8}in the ratio k:1

then____ X{9k-1/k+1}, Y{8k+3/k+1}

x-y+2=0

9k-1/k+1-8k+3/k+1+2=0

9k-1-8k-3+2k+2=0

3k-2=0 k=2/3