UPSC NDA Math Model Paper 2

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)=(

mx2+nx1

m+n

,

my2+ny1

m+n

)
⇒C=(

5m−1

m+1

,

7m+1

m+1

)
∵ 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

m+1

+

7m+1

m+1

=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