• # 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) $(4,\,\,1)$ C) $(1,\,\,1)$                                         D) $(4,\,\,4)$

Key Idea: The diagonals of a parallelogram bisects each other. Let the coordinate of fourth vertex be$({{x}_{1}},\,\,{{y}_{1}})$. $\therefore$Mid-point of$AC$is$(3,\,\,-2)$and mid-point of $DB$ is $\left( \frac{{{x}_{1}}+2}{2},\,\,\frac{{{y}_{1}}-5}{2} \right)$. Since, the diagonals, of a parallelogram bisects each other. $\therefore$  $\frac{{{x}_{1}}+2}{2}=3$and$\frac{{{y}_{1}}-5}{2}=-2$ $\Rightarrow$               ${{x}_{1}}=4$and${{y}_{1}}=1$ $\therefore$Required coordinates is$(4,\,\,1)$.