In what ratio is the line joining the points A (- 1, 1) and B (5, 7) divided by the line x + y = 4?

CONCEPT:

Let A (x1, y1) and B (x2, y2) be the two given points and the point P (x, y) divide the line joining the points A and B in the ratio m : n, then

• Point of internal division is given as: 
• Point of external division is given as: 

Note: If P is the mid-point of line segment AB, then 

CALCULATION:

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: 

∵ 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.

⇒ (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.