Question

A parallelogram has vertices $A(4,4,-1),B(5,6,-1),C(6,5,1),D(x,y,z)$. Then the vertex $D$ is

• A. $(5,1,0)$
• B. $(-5,0,1)$
• C. $(5,3,1)$
• D. $(5,1,3)$

Answer 1

Answer: (C)

$(5,3,1)$

Diagonals of a parellelogram bisect each other

=> O is the mid-point of AC and BD.

Using mid-point formula, coordinates of O are $(\frac{6+4}{2},\frac{5+4}{2},\frac{1+(-1)}{2})=>(5,\frac{9}{2},0)$

Applying mid point formula on diagonal BD, we get coordinates of D as $(5,3,1)$