Question

The coordinates of three consecutive vertices of a parallelogram are $(1,3),(-1,2)$ and $(2,5).$ The coordinates of the fourth vertex are

• A. $(6,4)$
• B. $(4,6)$
• C. $(-2,0)$
• D. none of these

Answer 1

The correct option is B $(4,6)$

Let the parallelogram be $ABCD$ and $O$ is the midpoint of both diagonals $AC$ and $DB$
So, $AO=OC$ and $DO=OB$.

Let $A(1,3),B(-1,2),C(2,5)$ and $D(x,y)$
As $AO=OC$, $O$ is mid point of $AC$,

$h=\frac{1+2}{2},k=\frac{3+5}{2}$

$\Rightarrow h=3/2,k=4$
Hence, coordinate of $O$ is $(3/2,4)$.

Now, $BO=OD$

so by midpoint formula i.e,

$3/2=(x+(-1\left)\right)/2$ and $4=(y+2)/2$ from these equations we get calculate x and y
So, the coordinates of $D$ are $(4,6)$.