Question

18. The line 3x + y - 9 = 0 divides the
line joining the points (1.3) and (2.7)
internally in the ratio *​

Answer 1

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then (x,y)=(m+nmx2+nx1,m+nmy2+ny1)

Let the ratio be k:1

Substituting (x1,y1)=(1,3) and (x2,y2)=(2,7) in thesection formula, we get the point which divides as (k+1k(2)+1(1),k+1k(7)+1(3))=(k+12k+1,k+17k+3)

Since this point lies on the line 3x+y−9=0, we have

3(k+12k+1)+k+17k+3−9=0

=>6k+3+7k+3−9k−9=0

4k−3=0

k=43

Hence, the ratio is a:b=3:4 internally.

So a+b=7