Straight Line Question 40

Question: If the given lines $ y=m_1x+c_1,y=m_2x+c_2 $ and $ y=m_3x+c_3 $ be concurrent, then

Options:

A) $ m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0 $

B) $ m_1(c_2-c_1)+m_2(c_3-c_2)+m_3(c_1-c_3)=0 $

C) $ c_1(m_2-m_3)+c_2(m_3-m_1)+c_3(m_1-m_2)=0 $

D)None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • $ \begin{vmatrix} m_1 & -1 & c_1 \\ m_2 & -1 & c_2 \\ m_3 & -1 & c_3 \\ \end{vmatrix} =0 $
    Þ $ m_1(c_2-c_3)+m_2(c_3-c_1)+m_3(c_1-c_2)=0 $ .Note: Students should remember this question as a formula.