In what ratio of line x-y-2=0 divides the line segment joining (3,-1)and (8,9)​

The ratio in which the line x-y-2=0 divides the line joining A(3,-1) and B(8,9) is in the ratio 2:3

Step-by-step explanation:

Let (x, y) be the coordinates of point of intersection.

Hence x=(a*8+1*3)(a+1) = (8a+3)/(a+1)

and

y = {a*9+1*(-1)}/(a+1)=(9a-1)/(a+1)

Since this point lies on the line x-y-2=0

Hence (8a+3)/(a+1)-(9a-1)/(a+1)-2=0

i.e. 8a+3–9a+1–2(a+1)=0

Or 8a+3–9a+1–2a-2=0

i.e.-3a+2=0

Hence a=2/3

hence the ratio in which the line x-y-2=0 divides the line joining A(3,-1) and B(8,9) in the ratio 2/3:1

i.e. 2:3