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SSC Quantitative Aptitude Coordinate Geometry Question Bank Coordinate Geometry and Graphs of Linear Equations (I)

  • question_answer
    The vertices of a triangle are\[A\,(4,4),\]\[B\,(3,-2)\]and\[C\,(-\,3,16).\]The area of the triangle is

    A) 36 sq units

    B) 37 sq units

    C) 38 sq units

    D) None of these

    Correct Answer: D

    Solution :

    [d] Here \[{{x}_{1}}=4,\]\[{{x}_{2}}=3,\]\[{{x}_{3}}=-\,3,\]\[{{y}_{1}}=4,\]\[{{y}_{2}}=-2\]and \[{{y}_{3}}=16.\] \[\Delta =\frac{1}{2}\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}\] \[=\frac{1}{2}\{4\,(-2-16)+3\,(16-4)-3\,(4+2)\}\] \[\frac{1}{2}\left| \{-72+36-18\} \right|=27\,\]sq unite


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