#1**+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

#1**+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