Question

If $A,B,C,D$ are the mid points of the sides of a quadrilateral PQRS in that order. If the co ordinates of $A,B,C,D$ are $(0,1),(3,4),(4,6)$ and $(a,b)$ respectively then

• A. $a=1,b=3$
• B. $a=1,b=2$
• C. $a=2,b=4$
• D. $a=2,b=3$

Answer 1

The correct option is A $a=1,b=3$

We know that,line joining mid points of two sides of triangle is parallel to third side of triangle.
$\therefore$ Assuming diagonals of quadrilateral as third side of triangle ,

we get slope of Line AB = slope of Line CD $⟹\frac{b-6}{a-4}=1⟹b-2=a$...........(1)
And also from other diagonal ,slope of Line AD= slope of Line BC $⟹\frac{b-1}{a}=2⟹2a=b-1$.................(2)
From (1) and (2) ,we get $a=1$ and $b=3$.