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

  • question_answer
    If the points \[A\,(1,-1),\]\[B\,(5,2)\] and \[C\,(k,5)\]are collinear, then k is equal to

    A) 2

    B) 4

    C) 6

    D) 9

    Correct Answer: D

    Solution :

    [d] Given,\[{{x}_{1}}=1,\]\[{{x}_{2}}=5,\]\[{{x}_{3}}=k\] \[{{y}_{1}}=-1,\] \[{{y}_{2}}=2,\] \[{{y}_{3}}=5\] Since, A, B and C are collinear, \[\therefore \]      \[\Delta =0\] \[\Rightarrow \]\[\{{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})\}=0\] \[\Rightarrow \]   \[\{1\,(2-5)+5\,(5-(-1)+k\,(-1-2)\}=0\] \[\Rightarrow \]   \[\{-3+30-3k\}=0\] \[\therefore \]      \[k=9\]


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