Explanation:
The coordinates are given below as
[tex]\begin{gathered} Q(-6,11) \\ R(2,-1) \\ S(-4,8) \\ T(-1,10) \end{gathered}[/tex]
Concept:
Rule for perpendicularity,
[tex]m_1\times m_2=-1[/tex]
Rule for parallelism
[tex]m_1=m_2[/tex]
Step 1:
We will calculate the slope of QR using the formula below
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} m_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m_1=\frac{-1-11}{2-(-6)} \\ m_1=-\frac{12}{2+6} \\ m_1=-\frac{12}{8} \\ m_1=-\frac{3}{2} \end{gathered}[/tex]
Step 2:
Calculate the slope of RT using the formula below
[tex]\begin{gathered} m_2=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} m_2=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m_2=\frac{10-8}{-1-(-4)} \\ m_2=\frac{2}{-1+4} \\ m_2=\frac{2}{3} \end{gathered}[/tex]
Hence,
[tex]\begin{gathered} m_1\ne m_2(not\text{ }parllel) \\ m_1\times m_2=-\frac{3}{2}\times\frac{2}{3}=-1 \end{gathered}[/tex]
Hence,
The final answer is
[tex]Perpendicular[/tex]
