Question

The three vertices of a parallelogram PQRS are P(3,-1,2), Q(1,2,-4), R(-1,1,2). Then, the coordinates of the fourth vertex is .

• A. (-1,-2,8)
• B. (1, 2,8)
• C. (1,-2,8)
• D. (1,-2,-8)

Answer 1

The correct option is C (1,-2,8)

Let the coordinates of the fourth vertex S be (x,y,z).
Since, the diagonals of a parallelogram bisect each other.
So,the mid-points of PR and QS will coincide.
$\therefore (\frac{3-1}{2},\frac{-1+1}{2},\frac{2+2}{2})=(\frac{1+x}{2},\frac{2+y}{2},\frac{-4+z}{2})\Rightarrow (1,0,2)=(\frac{x+1}{2},\frac{y+2}{2},\frac{z-4}{2})\Rightarrow \frac{x+1}{2}=1,\frac{y+2}{2}=0\mathrm{and}\frac{z-4}{2}=2\Rightarrow x=1,y=-2\mathrm{and}z=8$