Question

Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 4. A(2, 3), B(-1, 4), C(-5,3), D(-4, 6)m(AB) m(CD) Types of LinesEnter text

Answer 1

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

`m_1=(2--1)/(3-4)=-3`

And the slope m_2 of the line CD is

`m_2=(-5--4)/(3-6)=(1)/(3)`

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.