Question

Find the ratio in which x-y-2=0 divides the line segment joining the point a (3, -1) and b (8, 9)

Answer 1

Let the line x-y-2=0 divides the line segment joining (3, -1) and (8, 9) in the ratio m:n at c(x, y)

then,

c(x, y) =((8m+3n) /m+n, (9m-n) /m+n)

now,

this point must lie on x-y-2=0, so

((8m+3n) /m+n) -((9m-n) /m+n) -2=0

=> (8m+3n) -(9m-n) -2(m+n) =0

=> -3m+2n=0

=> 3m=2n or m/n = 2/3

or m:n = 2:3