Question

If there consecutive vertices of a parallelogram are $(1,-2)$, $(3,6)$ and $(5,10)$, then its fourth vertex is

• A. $(2,-3)$
• B. $(-2,-3)$
• C. $(3,2)$
• D. $(3,-2)$

Answer 1

Answer: (C)

$(3,2)$

Let the vertices of the parallelogram be A$(1,-2)$, B$(3,6$), C$(5,10)$ and D $(x,y)$ Since diagonals of a parallelogram bisect each other, mid-point of AC= mid-point of BD
$\Rightarrow (\frac{5+1}{2},\frac{10-2}{2})=(\frac{x+3}{2},\frac{y+6}{2})\Rightarrow (3,4)=(\frac{x+3}{2},\frac{y+6}{2})$
$\Rightarrow x=3,y=2$.