Question

If $(3,4)$ and $(6,5)$ are the extremities of a diagonal of a parallelogram and $(2,1)$ is its third vertex, then its fourth vertex is

• A. $(-1,0)$
• B. $(-1,1)$
• C. $(0,-1)$
• D. $(7,8)$

Answer 1

Answer: (D)

$(7,8)$

Mid-point of $(3,4)$ and $(6,5)$ is $(\frac{9}{2},\frac{9}{2})$
This is also mid point of diagonal joining third vertex $(2,1)$ and fourth vertex $(x,y)$
Then,
$\frac{9}{2}=\frac{x+2}{2},\frac{9}{2}=\frac{y+1}{2}\Rightarrow x=7,y=8$