Question

If $(1,2),(4,y),(x,6)$ and $(3,5)$ are the vertices of a parallelogram taken in order find $xandy$

• A. $x=3,y=6$
• B. $x=-6,y=3$
• C. $x=6,y=3$
• D. $x=3,y=-6$

Answer 1

Answer: (C)

$x=6,y=3$

Coordinates of M are mid points of BD

$\therefore M=(\frac{4+3}{2},\frac{5+y}{2})$

Coordinates of M are mid points of AC

$\therefore M=(\frac{1+x}{2},\frac{2+6}{2})$

$\therefore \frac{1+x}{2}=\frac{y+3}{2}sox=6\frac{5+y}{2}=\frac{2+6}{2}\therefore y=3$