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Question

The ratio in which x axis divides the line segment joining the points (6 , 4) and (1 ,- 7) is m : n. Find the value of mn.
  1. 50
  2. 45
  3. 36
  4. 28


Solution

The correct option is D 28
Let p(x,0) be the point on the x axis.

Let k : 1 be the ratio of the line segment joining the points (6,4) and (1,-7) and

 The coordinates of P (x, 0) are
p(x,0)=(1×k+1×6k+1,k×7+1×4k+1)           =(k+6k+1,7k+4k+1)

 7k+4=0

 k=47.

Hence, k : 1 = m : n = 47 : 1 
                               = 4 : 7

Therefore, mn = 4 x 7 = 28

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