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

  • question_answer
    Three vertices of a parallelogram taken in order are \[(-1,-6),\] \[(2,-5)\] and \[(7,2)\]. The fourth vertex is:

    A) \[(1,4)\]

    B) \[(1,1)\]

    C) \[(4,4)\]

    D) \[(4,1)\]

    Correct Answer: D

    Solution :

    [d] Let fourth vertex be \[(x,y)\].
    Mid-points of diagonals coincide.
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,(3,-2)=\left( \frac{2+x}{2},\frac{-5+x}{2} \right)\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,3=\frac{2+x}{2}\] and \[-2=\frac{-5+y}{2}\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x=4,\,\,\,\,y=1\]


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