Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The question is

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

To get the answer I tried the distance formula, equated AB=CD and AC=BD.

share|improve this question
    
Doesn't this have more than one solution, depending on the order of the vertices in the parallelogram or is D meant to be connected to A and C? –  martin.koeberl Dec 19 '12 at 8:35
    
A upper left, B upper right, C lower right, D lower left. –  chndn Dec 19 '12 at 8:38

2 Answers 2

If you have a parallelogram ABCD, then you know the vectors $\vec{AB}$ and $\vec{DC}$ need to be equal as they are parallel and have the same length. Since we know that $\vec{AB}=(-2,\,3,-6)$ you can easily calculate $D$ since you (now) know $C$ and $\vec{CD}(=-\vec{AB})$. We get for $\vec{0D}=\vec{0C}+\vec{CD}=(-1,\,1,\,2)+(\,2,-3,\,6)=(\,1,-2,\,8)$ and hence $D(\,1,-2,\,8)$.

share|improve this answer

You don't need to consider distance. You need to compute the difference vecotrs between adjacent sides. For instance, compute the difference vector from $B$ to $A$ and then add that to $C$.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.