A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1 4 . Three stones A , B and C are placed at the points 1 , 1 , 2 ,

Question

A man is walking on a straight line. The arithmetic mean of the reciprocals of the intercepts of this line on the coordinate axes is 1 4 . Three stones A , B and C are placed at the points 1 , 1 , 2 , 2 and 4 , 4 respectively. Then which of these stones is / are on the path of the man?

TestHub · Accepted Answer

Let the line be y = m x + c x - intercept : - c m y - intercept : c A . M of reciprocals of the intercepts : - m c + 1 c 2 = 1 4 ⇒ 2 1 - m = c line : y = m x + 2 1 - m = c ⇒ y - 2 - m x - 2 = 0 ⇒ line always passes through 2 , 2

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