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NotTheSmartest  Mar 7, 2017

Best Answer 

 #1
avatar+4806 
+6

I remember doing these D:

 

The slope of AB must match the slope of CD.

The slope of BC must match the slope of AD.

 

Slope of AB =  \(\frac{-1-6}{-5+9}=-\frac{7}{4}\)

Slope of CD = \(\frac{5+2}{-1-3}=-\frac{7}{4}\)

 

Slope of BC = \(\frac{6-5}{-9+1}=-\frac{1}{8}\)

Slope of AD = \(\frac{-1+2}{-5-3}=-\frac{1}{8}\)

 

So far so good. We have just shown that this is a parallelogram at least.

In order for it to be a rhombus:

 

The slope of BD must be the negative reciprocal of the slope of AC.

 

Slope of BD = \(\frac{6+2}{-9-3}=-\frac{8}{12}=-\frac{2}{3}\)

Slope of AC = \(\frac{-1-5}{-5+1}=\frac{-6}{-4}=\frac{3}{2}\)

 

Everything checks out. This figure is infact a rhombus. :)

hectictar  Mar 7, 2017
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2+0 Answers

 #1
avatar+4806 
+6
Best Answer

I remember doing these D:

 

The slope of AB must match the slope of CD.

The slope of BC must match the slope of AD.

 

Slope of AB =  \(\frac{-1-6}{-5+9}=-\frac{7}{4}\)

Slope of CD = \(\frac{5+2}{-1-3}=-\frac{7}{4}\)

 

Slope of BC = \(\frac{6-5}{-9+1}=-\frac{1}{8}\)

Slope of AD = \(\frac{-1+2}{-5-3}=-\frac{1}{8}\)

 

So far so good. We have just shown that this is a parallelogram at least.

In order for it to be a rhombus:

 

The slope of BD must be the negative reciprocal of the slope of AC.

 

Slope of BD = \(\frac{6+2}{-9-3}=-\frac{8}{12}=-\frac{2}{3}\)

Slope of AC = \(\frac{-1-5}{-5+1}=\frac{-6}{-4}=\frac{3}{2}\)

 

Everything checks out. This figure is infact a rhombus. :)

hectictar  Mar 7, 2017
 #2
avatar+77218 
+5

Well-presented, hectictar....!!!

 

 

cool cool cool

CPhill  Mar 7, 2017

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