Question

$A(-1,0),B(1,3)$ and $D(3,5)$ are the vertices of a parallelogram $ABCD$. Find the coordinates of vertex $C.$

Answer 1

Let the co-ordinates of vertex $C$ be $(x,y).$

$ABCD$ is a parallelogram.

$\therefore$ Mid-point of $AC=$ Mid-point of $BD.$

$\Rightarrow$ $(\frac{-1+x}{2},\frac{0+y}{2})=(\frac{1+3}{2},\frac{3+5}{2})$

$\Rightarrow$ $(\frac{-1+x}{2},\frac{y}{2})=(2,4)$

$\Rightarrow$ $\frac{-1+x}{2}=2$ and $\frac{y}{2}=4$

$\Rightarrow$ $-1+x=4$ and $\frac{y}{2}=4$

$\Rightarrow$ $x=5$ and $y=8$

$\therefore$ The co-ordinates of vertex $C$ is $(5,8).$