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

If \[P(1,2),\] \[Q(4,6),\]\[R(5,7)\] and \[S(a,b)\] are the vertices of a parallelogram PQRS then:

A) \[a=2,\,b=4\]

B) \[a=3,\,b=4\]

C) \[a=2,\,b=3\]

D) \[a=3,\,b=5\]

Correct Answer: C

Solution :

[c] Daygrm

Mid-point of \[PR=\left( \frac{1+5}{2},\frac{2+7}{2} \right)=\left( 3,\frac{9}{2} \right)\]

Mid-points of \[SQ=\left( \frac{4+a}{2},\frac{6+b}{2} \right)\]

Diagonals of parallelogram bisect each other.

\[\therefore \,\,\,\,\,\,\,\,\,\,\left( 3,\frac{9}{2} \right)=\left( \frac{4+a}{2},\frac{6+b}{2} \right)\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,3=\frac{4+a}{2},\,\,\frac{9}{2}=\frac{6+b}{2}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,a=2,\,\,\,b=3.\]