Determine the ratio in which the line `3x+y-9=0` divides the segment joining the points (1,3) and `(2,7)dot`

Explanation

As we know the section formula that, if a point `(x,y) `divides the line joining the points `(x_1,x_2)` and,`(y_1,y_2)`in the ratio `m:n`, then

`(x,y)=((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n))`

Now let the line `3x+y−9=0 `divides the line segment joining `A(1,3)` and `B(2,7)` in the ratio `k:1` at point `C`.

Then coordinates of `C` are `((2k+1)/(k+1),(7k+1)/(k+1))`
But, `C` lies on `3x+y−9=0`

So,

` \Rightarrow 3((2k+1)/(k+1))+((7k+1)/(k+1))−9=0`

`\Rightarrow k=3/4`

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