A) \[4:1\]
B) \[1:2\]
C) \[1:3\]
D) \[3:1\]
Correct Answer: A
Solution :
Let points be \[A(-3,-1),B(a,b),\,C(3,3)\] and \[D(4,3)\]. So, coordinates of the mid-point of AC = coordinates of the mid-point of BD [\[\because \] In parallelogram, diagonals bisect each other] \[\Rightarrow \] \[\left( \frac{-3+3}{2},\frac{-1+3}{2} \right)=\left( \frac{a+4}{2},\frac{b+3}{2} \right)\] \[\Rightarrow \] \[(0,1)=\left( \frac{a+4}{2},\frac{b+3}{2} \right)\] \[\Rightarrow \] \[\frac{a+4}{2}=0\] and \[\frac{b+3}{2}=1\] \[\Rightarrow \] \[a=-4\] and \[b=-1\] Now, \[\frac{a}{b}=\frac{-4}{-1}=\frac{4}{1}\Rightarrow a:b=4:1\]
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