Question

Help me fill out these questions about the graphed rectangle

Answer 1

Step 1

Find the length of IJ

`\begin{gathered} IJ=\sqrt[]{(-3-(-6))^2+(0-(-5))^2} \\ IJ=\sqrt[]{34}=5.830952 \end{gathered}`

Find the length of JK

`\begin{gathered} JK=\sqrt[]{(-6-(-1))^2+(-5-(-8))^2} \\ JK=\sqrt[]{34}=5.830952 \end{gathered}`

Find the length of KL

`\begin{gathered} KL=\sqrt[]{(2-(-1))^2+(-3-(-8))^2} \\ KL=\sqrt[]{34}=5.830952 \end{gathered}`

Find the length of LI

`\begin{gathered} LI=\sqrt[]{(2-(-3))^2+(-3-0)^2} \\ LI=\sqrt[]{34}=5.830952 \end{gathered}`

Therefore all sides are of equal measure.

Step 2

Find the slope of IJ

`\text{Slope}=(5)/(3)`

Find the slope of JK

`\text{Slope}=(-3)/(5)`

Find the slope of KL

`\text{Slope}=(5)/(3)`

Find the slope of LI

`\text{Slope}=-(3)/(5)`

For perpendicular lines;

`\begin{gathered} m_2=-(1)/(m_1) \\ m_1=(5)/(3)_{} \\ -(1)/(m_1)=-(1)/((5)/(3))=-1*(3)/(5)=-(3)/(5) \end{gathered}`

Adjacent sides of the quadrilateral are perpendicular since all sides are equal.

Adjacent sides include; IJ and Jk, KL, and LI. The slopes of these sides as calculated above show that the lines are perpendicular.

Therefore, the slope of any pair of adjacent sides are negative reciprocals.

That being the case those sides are perpendicular

Therefore as a result of these two things taken together the quadrilateral is a square