10th Class Mathematics Coordinate Geometry Question Bank MCQs - Coordinate Geometry

If four vertices of a parallelogram taken in order are \[(-3,-1),\] \[(a,b),\] \[(3,3)\] and \[(4,3)\]. then \[a:b=\]

A) \[1:4\]

B) \[4:1\]

C) \[1:2\]

D) \[2:1\]

Correct Answer: B

Solution :

[b] Mid-point of AC = mid-point of BD

Let \[A(-3-1),\,B(a,b),\,C(3,3),\,D(4,3)\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(0,1)=\left( \frac{4+a}{2},\,\,\frac{3+b}{2} \right)\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a=-4,\,\,b=-1\]

\[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a:b=4:1\]