Question

Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,4) and C(-1,1,2). Find the fourth vertex .

• A. (1,0,2)
• B. (1,2,0)
• C. (2,1,0)
• D. (2,0,1)

Answer 1

The correct option is A

(1,0,2)

Let D(x,y,z) be the fourth vertex of the parallelogram.
The diagonals of a parallelogram bisect each other.
Therefore, the midpoints of AC and BD are the same. Let this be O.

$O=(\frac{3-1}{2},\frac{-1+1}{2},\frac{2+2}{2})O=(1,0,2)$

Now, O is the midpoint of BD
$\therefore \frac{1+x}{2}=1\Rightarrow x=1\frac{2+y}{2}=0\Rightarrow y=-2\frac{4+z}{2}=2\Rightarrow z=0$

D=(1,0,2)