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 $$14$$. 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?

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  $$14$$. 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?

Infinity Learn · Accepted Answer

$$xa+yb=1ha+kb=1----(1)1a+1b2=14$$∴$$1a+1b=12-----(2)$$∴  Line passes through fixed point (2$$,$$2).    (from$$ $$(1) and (2))

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 $\frac{1}{4}$ . 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?

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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 14. 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?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

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 $\frac{1}{4}$ . 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?