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Calculate the length of the parallelogram's diagonals.

According to my book, $å=|u-z|$, and not $|z+w|$. $|u-z| \neq |z+w|$.

Q: If I am wrong, why am I wrong and if so, why do you calculate $å$ as $|u-z|$ and not $|z+w|$?

Andreas
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1 Answers1

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Let the origin be $O(0,0)$. Then, it is easy to see that that $OUWZ$ is a parallelogram with $U(4,6) ; W(7,5) ; Z(3,-1)$.

Note that $$OZ = UW = \sqrt{3^2+1^2} = \sqrt{10}\, \text{ and } OU = WZ = \sqrt{4^2+6^2} = \sqrt{52}$$

Also, $$UZ = \sqrt{7^2+1^2} = \sqrt{50}$$

This implies that $UZ$ should be the diagonal, instead of $ZW$, right?

  • Hmm... are the diagonals of a parallelogram always equal? – Andreas Dec 27 '17 at 13:11
  • https://math.stackexchange.com/questions/1548490/why-are-the-diagonals-of-a-parallelogram-not-equal – Andreas Dec 27 '17 at 13:11
  • I think that one diagonal is of length $\sqrt74$, but another is of length $\sqrt50$. In which way, you offered me a new insight in how to view vectors so that was very helpful :). – Andreas Dec 27 '17 at 13:18
  • @AndreasAlmgren Thanks for correcting the typo. And yes, the diagonals of a parallelogram are not equal, but in the case they are, then it becomes a rectangle, right? –  Dec 27 '17 at 13:22