Straight Line Question 370

Question: The base BC of a triangle ABC is bisected at the point (p, q) and the equations to the sides AB and AC are respectively $ x+y+3=0 $ and $ qx+py=1. $ Then the equation to the median through A is

Options:

A) $ 2x-y=9 $

B) $ (p^{2}+q^{2}-1)(px+qy-1)=(2p-1)(qx+py-1) $

C) $ (pq-1)(px+qy-1)=(p^{2}+q^{2}-1)(qx+py-1) $

D)None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • Since the median passes through A, the intersection of the given lines. Its equation is given by $ (px+qy-1)+\lambda (qx+py-1)=0 $ , where $ \lambda $ is some real number. Also, since the median passes through the point (p, q), we have $ (p^{2}+q^2-1)+\lambda (pq+pq-1)=0 $ Þ $ \lambda =-\frac{p^{2}+q^{2}-1}{2pq-1} $ and the equation of median through A is $ (px+qy-1)-\frac{p^{2}+q^{2}-1}{2pq-1}(qx+py-1)=0 $
    Þ $ (2pq-1)(px+qy-1)=(p^{2}+q^{2}-1)(qx+py-1) $ .



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