Question

$A(-1,2),B(4,1)andC(7,6)$ are three vertices of the parallelogram $ABCD$. The coordinates of fourth vertex is _______.

• A. $(7,-2)$
• B. $(-2,7)$
• C. $(7,2)$
• D. $(2,7)$

Answer 1

Answer: (D)

$(2,7)$

Let the three vertices of parallelogram ABCD be $A(-1,2),B(4,1)andC(7,6)$

Let the fourth vertex be $D(a,b)$

By joining AC and BD intersect at point O i.e, diagonals of parallelogram bisect each other

Mid point of AC= $(\frac{-1+7}{2},\frac{2+6}{2})=(3,4)$

Mid point of BD $=(\frac{4+a}{2},\frac{1+b}{2})\frac{4+a}{2}=3\frac{1+b}{2}=4\therefore a=2,b=7$

$\therefore$ The coordinate of fourth vertex =$(2,7)$