Question

determine the ratio in which Y - X + 2 = 0 divides the line joining (3 ,- 1) and (8, 9)

Answer 1

let when line y-x+2=0 divides the ratio in k:1
x=(8k+3)/k+1, y=(9k-1)/k+1
these points must satisfies the eqaution
(9k-1)/(k+1) +2=(8k+3)/k+1
11k+1=8k+3
k=2/3
the lines divides tle joining two points is 2:3

Answer 2

hope this ll help and i solved eq. of 2 lines to get pt of intersection also if it isnt clear in the picture ... k is required ratio