Question

(a) Draw $x$ and $y$ axes and mark the points $A(2,0),B(5,0)$ and $C(7,3)$.
(b) If $ABCD$ is a parallelogram, write the co-ordinates of $D$.
(c) Draw the parallelogram $ABCD$.

Answer 1

(b)Let the co-ordinates of $D$ be $(x,y)$
$A=(2,0),B(5,0)$ and $C(7,3)$
As diagonals of parallelogram bisect each other.
Mid-point of $AC=$ mid-point of $BD$
Now, co-ordinates of $AC=(\frac{2+7}{2},\frac{0+3}{3})=(\frac{9}{2},\frac{3}{2})$
Co-ordinates of $BD=(\frac{x+5}{2},\frac{y+0}{2})$
$\frac{x+5}{2}=\frac{9}{2}\frac{y}{2}=\frac{3}{2}$
$\Rightarrow$ $x=4$ and $y=3$
Thus, co-ordinates of $D$ are $(4,3)$