Question

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

Answer 1

Answer:

2:3

Step-by-step explanation:

Let A=(3,-1) B=(8,9)

Let the line x-y-2=0 divide the line segment AB at point C(x,y) in the ratio m:n

By section formula,

C(x,y)=[m*8+n*3/m+n , m*9+n*(-1)/m+n]=[8m+3n/m+n , 9m-n/m+n]

Since point C(x,y) lie on line x-y-2=0,

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

8m+3n -9m+n -2m -2n = 0

-3m + 2n = 0

3m = 2n

m/n = 2/3

Hence, line x-y-2=0 divide the line segment joining A(3,-1) & B(8,9) in the ratio 2:3