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SSC Sample Paper Mock Test-13 SSC CGL Tear-II Paper-1

  • question_answer
    Find the value of k for which the pointe \[A\,\,(-1,3),\]\[B\,\,(2,k)\] and \[C\,\,(5,-1)\] are collinear

    A) 0

    B)  2      

    C) \[-\,\,1\]

    D)  1

    Correct Answer: D

    Solution :

    Here \[{{x}_{1}}=-1,\]\[{{x}_{2}}=2,\]\[{{x}_{3}}=5\]and \[{{y}_{1}}=3,\]\[{{y}_{2}}=k\]and \[{{y}_{3}}=-1.\] Now, \[\Delta =0\]\[\Leftrightarrow \]\[{{x}_{1}}({{y}_{2}}-{{y}_{3}})+{{x}_{2}}({{y}_{3}}-{{y}_{1}})+{{x}_{3}}({{y}_{1}}-{{y}_{2}})=0\] \[\Leftrightarrow \]\[-1.(k+1)+2(-1-3)+5(3-k)=0\] \[\Leftrightarrow \]\[-k-1-8+15-5k=0\]\[\Leftrightarrow \]\[6\]\[\Leftrightarrow \]\[k=1.\] Hence, \[k=1.\]


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