We can calculate the slope as:
[tex]S=\frac{{\Delta}Y}{\Delta X}[/tex]
From this, we have: (FIRST ANSWER)
[tex]\begin{gathered} S_{ZY}=\frac{0-\mleft(-3\mright)}{1-6}=-\frac{3}{5} \\ S_{YX}=\frac{-6-(-3)}{1-6}=\frac{3}{5} \\ S_{XW}=\frac{-3-(-6)}{-4-1}=-\frac{3}{5} \\ S_{WZ}=\frac{-3-0}{-4-1}=\frac{3}{5} \end{gathered}[/tex]
The length of the non-parallel sides can be measured as:
[tex]L=\sqrt[]{(\Delta Y)^2+(\Delta X)^2}[/tex]
From this, we have: (SECOND ANSWER)
[tex]\begin{gathered} L_{ZW}=\sqrt[]{(1-(-4))^2+(0-(-3))^2}_{}=\sqrt[]{25+9}=\sqrt[]{34} \\ L_{ZY}=\sqrt[]{(6-1)^2+(-3-0)^2}=\sqrt[]{25+9}=\sqrt[]{34} \end{gathered}[/tex]
From the figure in the beginning and the values we found, this is a Rhombus.
