If the line 2 x+y=k passes though the point which divides the line segment joining the points (1,1) and (2,4) internally in the ratio 3: 2 then, (k+1):(k-1)=

Step-by-step solution

The coordinates of the point dividing the line segment joining (1,1) and (2,4) in the ratio 3:2 are given by the section formula: x = mx₂ + nx₁ m+n and y = my₂ + ny₁ m+n . Substituting x₁=1 , y₁=1 , x₂=2 , y₂=4 , m=3 , n=2 yields the point ( 8 5 , 14 5 ) . Since this point lies on the line 2x + y = k , substitution gives 2 8 5 + 14 5 = 30 5 = k , so k=6 . The ratio (k+1):(k-1) = 7:5 . The final answer is B .