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).