We are given coordinates of A, B, C and D :
A(2, 4), B(9, 8), C(-1, 2), and D(3, -5).
Now, we need to find the slopes of AB and CD.
Slope of AB is :
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(2,\:4\right),\:\left(x_2,\:y_2\right)=\left(9,\:8\right)[/tex]
[tex]m=\frac{8-4}{9-2}[/tex]
[tex]m=\frac{4}{7}[/tex].
Slope of CD is:
[tex]m=\frac{-5-2}{3-\left(-1\right)}[/tex]
[tex]m=-\frac{7}{4}[/tex].
Slope of CD is negative reciprocal of slope of slope of AB.
Therefore, lines AB are CD are perpendicular.
