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  5. Coordinate Geometry

10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

  • question_answer
    If points \[A(5,p),\] \[B(1,5),\] \[C(2,1)\] and \[D(6,2)\] form a square A6CD, then \[p=\]

    A) 7

    B) 3

    C) 6

    D) 8

    Correct Answer: C

    Solution :

    [c] Since ABCD is a square.
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,AB=AD\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,A{{B}^{2}}=A{{D}^{2}}\]
    \[\Rightarrow \,\,\,\,\,\,{{(1-5)}^{2}}+{{(5-p)}^{2}}={{(6-5)}^{2}}+{{(2-p)}^{2}}\]
    \[\Rightarrow \,\,\,16+25-10p+{{p}^{2}}=1+4-4p+{{p}^{2}}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,6p=36\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,p=6\]


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