We need to calculate the equation of the segment AB, First, we need to calculate the slope
(-3, 8) =(x1,y1)
(2,3) =(x2,y2)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-8}{2+3}=\frac{-5}{5}=-1[/tex]the equation is
[tex]\begin{gathered} y-8=-1(x+3) \\ y-8=-x-3 \\ y=-x-3+8 \\ y=-x+5 \end{gathered}[/tex]then we will calculate the same for the segment CD
(-4, 6) =(x1.y1)
(-8, 2) =(x2,y1)
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-6}{-8+4}=\frac{-4}{-4}=1[/tex]the equation is
[tex]\begin{gathered} y-6=1(x+4) \\ y-6=x+4 \\ y=x+4+6 \\ y=x+10 \end{gathered}[/tex]with the slopes, we can notice
mAB=-1
mCd= 1
because the slopes are inverse between each other, we can assume the lines given are perpendicular
