question_answer

Two sides of a parallelogram are along the lines,\[x+y=3\,\,\,\And \,\,x-y+3=0\]. If its diagonals intersect at (2, 4), then one of its vertex is- [JEE Main Online Paper (Held On 10-Jan-2019 Evening]

A) (2, 1)                            

B) (2, 6) 

C) (3, 5)    

D)                  (3, 6)

Correct Answer: D

Solution :

Slope of \[BC=1\] \[\Rightarrow \,\,\,\frac{3-h-5}{h-4}\,\,=\,\,1\,\,\Rightarrow \,\,h\,\,=\,\,1\,\,\,\Rightarrow \,\,B(1,\,\,2)\] Now, E is the mid-point of BD so D(3, 6)