Let:
A=(-4,10)=(x1,y1)
B=(-8,1)=(x2,y2)
[tex]m_{AB}=\frac{1-10}{-8-(-4)}=\frac{-9}{-4}=\frac{9}{4}=2.25[/tex]C=(-5,7)=(x1',y1')
D=(-2,4)=(x2',y2')
[tex]m_{CD}=\frac{y2^{\prime}-y1^{\prime}}{x2^{\prime}-x1^{\prime}}=\frac{4-7}{-2-(-5)}=-\frac{3}{3}=-1[/tex]E=(2,-3)=(x1'',y1'')
F=(6,-7)=(x2'',y2'')
[tex]m_{EF}=\frac{y2^{\doubleprime}-y1^{\doubleprime}}{x2^{\doubleprime}-x1^{\doubleprime}}=\frac{-7-(-3)}{6-2}=\frac{-4}{4}=-1[/tex]Since:
[tex]\begin{gathered} m_{CD}=m_{EF} \\ -1=-1 \end{gathered}[/tex]The lines CD and EF are parallel
