Straight Line Question 141

Question: The lines y $ y=m_1x, $ $ y=m_2x, $ and $ y=m_3x, $ make equal intercepts on the line $ x+y=1 $ . Then

Options:

A) $ 2(1+m_1)(1+m_3)=(1+m_2)(2+m_1+m_3) $

B) $ (1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3) $

C) $ (1+m_1)(1+m_2)=(1+m_3)(2+m_1+m_3) $

D) $ 2(1+m_1)(1+m_3)=(1+m_2)(1+m_1+m_3) $

Show Answer

Answer:

Correct Answer: A

Solution:

  • [a] Solving the equations of the liners, we get $ A\equiv ( \frac{1}{1+m_1},\frac{m_1}{1+m_1} ), $ $ C\equiv ( \frac{1}{1+m_3},\frac{m_3}{1+m_3} ) $ If AB=BC. Then the med pint of AC lies on $ y=m_2x $