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9th Class Mathematics Coordinate Geometry Question Bank Co-ordinate Geometry

  • question_answer
    The three vertices of parallelogram taken in order are \[\left( -\mathbf{2},\mathbf{0} \right)\left( \mathbf{6},\mathbf{2} \right)\] and \[(\mathbf{4},\mathbf{2})\] respectively. Find the co-ordinates of the fourth vertex,

    A)  \[\left( 4,\text{ }3 \right)\]                       

    B)  \[(-\,3,4)\]          

    C)  \[(3,\,-4)\]                     

    D)  \[\left( 4,\text{ }3 \right)\]

    Correct Answer: D

    Solution :

    (d): Co-ordinates of the mid-point of AC = Co-ordinates of the mid-point of BD: \[\Rightarrow \]\[(1,2)=\left( \frac{6+X}{2}\text{, }\frac{2+y}{2} \right)\] \[\Rightarrow \]\[\left( \frac{-2+4}{2},\frac{0+4}{2} \right)=\left( \frac{6+X}{2}\text{, }\frac{2+y}{2} \right)\] \[\Rightarrow \]\[\frac{6+x}{2}=1\] and \[\frac{y+2}{2}=2\]. \[\Rightarrow \] \[x=-4\] and \[y=3\] Hence, the fourth vertex of the parallelogram is\[\left( -4,\text{ }3 \right)\].


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