Using the distance formula with unknown points

cogaha

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Apr 10, 2013
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This is my first post here! I am trying to help my daughter with honors geometry.

The problem is to use the distance formula to prove that WXYZ is a rhombus. There is a diagram which I obviously can't reproduce here, but I can give the points. We know the distance formula, but because each point is missing a coordinate, we don't know how to proceed. Any help or suggestions are MUCH appreciated!

W is located at (a,0)
X is located at (0,b)
Y is located at (-a,0)
Z is located at (0,-b)
 
You will need the definition of a rhombus. Find it and quote it here, please.
 
Well, we know that a rhombus is a parallelogram with all sides congruent
 
I am thinking it through, and I wonder if I can just pick any value for a that I want -- and then -a has the negative value of that. Then because the diagonals would have to be congruent, b would have to be the same as a, and -b equal to -a. Is that right?
 
Hello, cogaha!

Use the distance formula to prove that WXYZ is a rhombus.\displaystyle \text{Use the distance formula to prove that }WXYZ\text{ is a rhombus.}
The four vertices are: W(a,0),  X(0,b),  Y(-a,0),  Z(0,-b)\displaystyle \text{The four vertices are: }\:W(a,0),\;X(0,b),\;Y(\text{-}a,0),\;Z(0,\text{-}b)
Can you apply the Distance Formula to: .W(a,0) and X(0,b)?\displaystyle W(a,0)\text{ and }X(0,b)\,?

WX  =  (a0)2+(0b)2  =  a2+b2\displaystyle \overline{WX} \;=\;\sqrt{(a-0)^2 + (0-b)^2} \;=\;\sqrt{a^2+b^2}

Or is that too complicated for you?
 
Really?

Hi Soroban,

I really hope you didn't mean this the way it came across! I came to this forum to get help because I am not good at math and my daughter is having a very rough semester -- all I wanted to do was get help. If I knew how to do the problem already, I wouldn't have needed this forum, and your "help" really came across to me as a put down. I am glad you are great at math -- I am great at lots of things too, but math just isn't one of them. However, I can assure you that when I try to help someone with something, I NEVER would say anything condescending. I hope you have a great day, and I hope that you will use your math gifts in the future to help others in a more positive and constructive way.
Hello, cogaha!


Can you apply the Distance Formula to: .W(a,0) and X(0,b)?\displaystyle W(a,0)\text{ and }X(0,b)\,?

WX  =  (a0)2+(0b)2  =  a2+b2\displaystyle \overline{WX} \;=\;\sqrt{(a-0)^2 + (0-b)^2} \;=\;\sqrt{a^2+b^2}

Or is that too complicated for you?
 
Then because > > the diagonals would have to be congruent < < , b would have to be the same as a, and -b equal to -a. Is that right?
cogaha, the diagonals of a rhombus are never congruent, except in the case where in addition to it being a rhombus, it is also a square.
 
Hello, cogaha!

Sorry ... I thought I was being funny ... okay, maybe a bit sarcastic.

You had said, "Each point is missing a coordinate".
Not true . . . each point had two coordinates: (a,0), (0,b), (-a,0), (0,-b).

You gave the impression that you thought that math had to be in numbers,
. . that variables (letters) don't count.
If that's true, you and your daughter are still in Arithmetic
. . and not doing Algebra at all.

My remark could have been worded better.
It was meant as a wake-up call ... not a put-down.

I had hoped you'd read my explanation
. . and say, "Hey, of course!"

Again, I'm sorry that I offended you.
. . That certainly was not my intent.
 
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