Question

If $(1,-1,0),(-2,1,8)$ and $(-1,2,7)$ are three consecutive vertices of a parallelogram then the fourth vertex is

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

Answer 1

The correct option is A $(2,0,-1)$

Let the fourth vertex be $(h,k,l)$

The midpoints of diagonal will be same

The midpoints are $(0,\frac{1}{2},\frac{7}{2})$ and $(\frac{h-2}{2},\frac{k+1}{2},\frac{l+8}{2})$

If we equate both we get $h-2=0,k+1=1,l+8=7$

$\Rightarrow h=2,k=0,l=-1$

So the fourth vertex is $(2,0,-1)$