Question

In the diagram, point P and Q are the vertices of a quadrilateral PQRS.
Given that the coordinates of R and S are (8,0) and (4, -2) respectively, the figure PQRS is likely to be a:

• A. parallelogram
• B. rhombus
• C. trapezium
• D. kite

Answer 1

The correct option is A parallelogram

Slope of line $PQ=\frac{4-2}{8-4}=\frac{1}{2}$

As $P\equiv (4,2)$

and $Q\equiv (8,4)$

and slope of line $RS=\frac{-2-0}{4-8}=\frac{1}{2}$

As $R\equiv (8,0)$ and $S\equiv (4,-2)$

also $PR\parallel QS$

and as $PQ\parallel SR,$

we can say that $PQRS$ is likely to be a $parallelogram.$