Two lines are parallel if they have the same slope, and they are perpendicular if the slope of one is the negative of the reciprocal of the other.
The slope m_1 of the line AB is
[tex]m_1=\frac{2--1}{3-4}=-3[/tex]And the slope m_2 of the line CD is
[tex]m_2=\frac{-5--4}{3-6}=\frac{1}{3}[/tex]The slopes m_1 and m_2 are negative reciprocals of each other, meaning if you take the reciprocal of m_1 and then multiply it by -1, you will get m_2.
Hence, the lines are perpendicular.
