question_answer

If \[(-2,-1),\] \[(a,0),\] \[(4,b)\]and \[(1,2)\]are the vertices of a parallelogram, then the values of a and b are:

A) \[1,3\]

B) \[1,4\]

C) \[2,3\]

D) \[3,1\]

Correct Answer: A

Solution :

[a] The given points are \[A(-2,-1),\] \[B(a,0),\] \[C(4,b)\]and \[D(1,2)\].

Since the diagonals of a parallelogram bisect each other,

\[\therefore \]Coordinates of P are

\[X=\frac{-2+4}{2}=\frac{1+a}{2}\Rightarrow a=1\]

and       \[Y=\frac{-1+b}{2}=\frac{0+2}{2}\Rightarrow b=3\]