Here, we have to find the ratio in which the line x + y = 4 divides the line joining the points A (- 1, 1) and B (5, 7).
Let the line x + y = 4 divides the line joining the points A (- 1, 1) and B (5, 7) in the ratio m : 1
Let the point of division be C.
As we know that, the point internal division is given by:
(x,y)=(,) ⇒C=(,) ∵ C is the point of division i.e C lies on the line x + y = 4 and the coordinates of the point C will satisfy the equation of the line x + y = 4.
⇒+=4 ⇒ (5m - 1) + (7m + 1) = 4(m + 1)
⇒ m = 1/2
So, the required ratio is: (1/2) : 1 = 1 : 2
Hence, option B is the correct answer