Question

Three consecutive vertices of a parallelogram are $(-2,-1),(1,0)$ and $(4,3)$. Find the fourth vertex.

Answer 1

Diagonals of a parallelogram bisect each other,

let the point of intersection of diagonals be $M(m,n)$

$m=\frac{-2+4}{2}=1$ and $n=\frac{-1+3}{2}=1$

$\therefore m=1andn=1$

Let the Fourth vertex be $D(x,y)$

$\Rightarrow$ $m=\frac{1+x}{2}=1$ and $n=\frac{0+y}{2}=1$

$x+1=2$ and $y=2$

Thus $x=1$ & $y=2$

The fourth vertex of the parallelogram is $D\equiv (1,2)$