Question

If (3, 4), (5, 6) and (2, 8) are the three vertices of a parallelogram taken in order then the fourth vertex is ______________

• A. (6 , 0 )
• B. (0 , 6 )
• C. (0 , 0)
• D. (1, 5 )

Answer 1

The correct option is B (0 , 6 )

Diagonals of a parallelogram bisect each other. So the midpoint of opposite two vertices, will be same as the mid points of the other two opposite vertices
Let fourth vertex be $(x,y)$
Midpoint of the line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$
So midpoint of the diagonal 1 $=$ Midpoint of diagonal 2
$(\frac{3+2}{2},\frac{4+8}{2})=(\frac{5+x}{2},\frac{6+y}{2})$
Equating both the co-ordinates, we get
$5+x=5=>x=0$
And $6+y=12=>y=6$
So, the fourth vertex is $(0,6)$