Question

Fill out this whole column in an organized manner please

Answer 1

We can calculate the slope as:

`S=\frac{{\Delta}Y}{\Delta X}`

From this, we have: (FIRST ANSWER)

`\begin{gathered} S_(ZY)=(0-\mleft(-3\mright))/(1-6)=-(3)/(5) \\ S_(YX)=(-6-(-3))/(1-6)=(3)/(5) \\ S_(XW)=(-3-(-6))/(-4-1)=-(3)/(5) \\ S_(WZ)=(-3-0)/(-4-1)=(3)/(5) \end{gathered}`

The length of the non-parallel sides can be measured as:

`L=\sqrt[]{(\Delta Y)^2+(\Delta X)^2}`

From this, we have: (SECOND ANSWER)

`\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}`

From the figure in the beginning and the values we found, this is a Rhombus.