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#1 2008-01-26 02:17:48
- CatherineMorland
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Rhombus
Given points W(-0.5, 1.5), X(4, 1), Y(3.5, 5.5), Z(-1, 6), show that WXYZ is a rhombus.
#2 2008-01-26 04:48:44
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: Rhombus
A rhombus is a quadrilateral whose sides are all the same length.
Therefore, to show that WXYZ is a rhombus, you need to show that WX = XY = YZ = ZW.
You can do that using Pythagoras.
Why did the vector cross the road?
It wanted to be normal.
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#3 2008-01-26 05:04:15
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: Rhombus
I drew the 4 dots on paper.
It is a diamond shape or rhombus.
All sides are equal length.
I don't know the length yet,
but I know they are the same
because I can count the squares
going left and right and up and down
by 1/2 squares too.
Draw it and see if you
can find the middle of it?
I think the middle is
at (1.5, 3.5).
Do you know 45 degree
angles yet? If so,
look for these in
the picture.
A 45 degree angle is
a perfect diagonal
that is not too steep
or too shallow.
Last edited by John E. Franklin (2008-01-26 05:04:41)
igloo myrtilles fourmis
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#4 2008-01-26 05:27:34
- CatherineMorland
- Guest
Re: Rhombus
A rhombus is a quadrilateral whose sides are all the same length.
Therefore, to show that WXYZ is a rhombus, you need to show that WX = XY = YZ = ZW.You can do that using Pythagoras.
But why don't you do it this way:
#5 2008-01-26 05:31:06
- CatherineMorland
- Guest
Re: Rhombus
Sorry, the last part should be
(dot product)#6 2008-01-26 05:33:03
- CatherineMorland
- Guest
Re: Rhombus
ARGHHHH!! I mean
#7 2008-01-26 06:06:57
- mathsyperson
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- Registered: 2005-06-22
- Posts: 4,900
Re: Rhombus
You could certainly do it that way, but I'd have thought my way was easier.
Why did the vector cross the road?
It wanted to be normal.
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#8 2008-01-26 06:20:04
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: Rhombus
Very nice.
There are 6 connecting lines, and you chose
two parallel sides and two perpendicular bisectors.
Notice also that if X and W had been
switched you would have done the
four sides of the rhombus and noticed they are
all the same size: +/- 4.5 and -/+ 0.5
Do you have a routine or algorithm that
specifies what order of the six you chose??
igloo myrtilles fourmis
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#9 2008-01-26 07:13:32
- JaneFairfax
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- Registered: 2007-02-23
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#10 2008-01-26 07:41:10
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: Rhombus
I guess when you find the two parallel vectors, you can choose the diagonals wisely
based on the numbers. Like if one vector is +1, +3, and the other one is -1, -3, then
you are on opposite corners. But if the vectors are both the same then they the vectors are
starting from adjacent corners.
What do you call a vector that is 180 degrees from another vector?
(Very nice photo of JB, by the way)
(Oh, I see, you posted about glaucoma, wow!!)
Last edited by John E. Franklin (2008-01-26 07:45:21)
igloo myrtilles fourmis
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#11 2008-02-01 06:17:41
- JaneFairfax
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- Registered: 2007-02-23
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Re: Rhombus
Yes, I posted about glaucoma. 
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