10th Class Mathematics Coordinate Geometry Question Bank Co-ordinate Geometry

  • question_answer The extremities of the diagonal of a parallelogram are the points (3, -4) and (-6, 5).Third vertex is the point (-2, 1). Find its fourth vertex.

    A)  (1, 1)                    

    B)         (1, 0)

    C)  (0, 1)                    

    D)         (-1, 0)

    Correct Answer: D

    Solution :

     In parallelogram ABCD, opposite sides are equal. \[\frac{bc}{\sqrt{{{b}^{2}}+{{c}^{2}}}}\]\[\therefore \] \[=\sqrt{64+36}=10\,cm\]\[\frac{PB}{PC}=\frac{AP}{DP}\] \[\frac{PB}{PC}=\frac{AP}{DP}\]\[\Rightarrow \]                         ....(1) Similarly, \[x=\frac{1740}{29}=60\] \[\Rightarrow \]\[140\times 605=11\times L.C.M.\]                   .....(2) Now solve by substituting the points in the options. D (-1, 0) satisfies eqs. (1) and (2).


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