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JEE Main & Advanced Mathematics Straight Line Question Bank Critical Thinking

  • question_answer
    A line L passes through the points (1, 1) and    (2, 0) and another line \[{L}'\] passes through \[\left( \frac{1}{2},0 \right)\] and perpendicular to L. Then the area of the triangle formed by the lines \[L,L'\] and y- axis, is                                      [RPET 1991]

    A)            15/8                                          

    B)            25/4

    C)            25/8                                          

    D)            25/16

    Correct Answer: D

    Solution :

               Here \[L\equiv x+y=2\]and\[{L}'\equiv 2x-2y=1\].                    Equation of y-axis is \[x=0\]                    Hence the vertices of the triangle are \[A(0,\,2),B\left( 0,-\frac{1}{2} \right)\] and\[C\left( \frac{5}{4},\frac{3}{4} \right)\]. Therefore, the area of the triangle is \[\frac{1}{2}\left| \,\begin{matrix}    0 & 2 & 1  \\    0 & -\frac{1}{2} & 1  \\    \frac{5}{4} & \frac{3}{4} & 1  \\ \end{matrix}\, \right|=\frac{25}{16}\].


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