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# Help. ​

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Help.

NotTheSmartest  Mar 7, 2017

#1
+5888
+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
Sort:

#1
+5888
+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
#2
+80851
+5

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

CPhill  Mar 7, 2017

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