Question

In what ratio does the point -4,6 divide the line segment joining the points A of -6,0 and B3,18?

Answer 1

Answer:

Let the line x-y-2=0 …… (i). divide the line segment joining A(3, -1) and B(8, 9) in the ratio a:1

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