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

  • question_answer
    The vertices of a triangle are\[A\,(3,8),\]\[B\,(-\,4,2)\]and \[C\,(5,-1).\]The area of \[\Delta ABC\]is

    A) \[28\frac{1}{2}\]sq units

    B) \[37\frac{1}{2}\]sq units

    C) 57 sq units

    D) 75 sq units

    Correct Answer: B

    Solution :

    [b] Here, \[{{x}_{1}}=3,\]\[{{x}_{2}}=-\,4,\]\[{{x}_{3}}=5,\]\[{{y}_{1}}=8,\]\[{{y}_{2}}=2\]and \[{{y}_{3}}=-1.\] \[\Delta =\frac{1}{2}\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}\] \[=\frac{1}{2}\{3\,(2+1)-4\,(-1-8)+5\,(8-2)\}\] \[=\frac{1}{2}\{9+36+30\}=\frac{75}{2}\] \[=37\frac{1}{2}\] sq units


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