Question

Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 10. A(3, 1), B(3,-4), C(-4,1), D (-4,5)m(AB) m(CD) Types of lines

Answer 1

Answer:

Neither parallel nor perpendicular

Explanations:

The points are:

A(3, 1), B(3,-4), C(-4,1), D (-4,5)

The slope of a line is given as:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`

The slope of the line AB, m(AB), with gthe points A(3, 1), B(3,-4) is given as:

`\begin{gathered} m(AB)\text{ = }(-4-1)/(3-3) \\ m(AB)\text{ = }(-5)/(0) \\ m(AB)\text{ =- }\infty \end{gathered}`

The slope of the line CD, m(CD), with the points C(-4,1), D (-4,5) is given as:

`\begin{gathered} m(CD)\text{ = }(5-1)/(-4-(-4)) \\ m(CD)\text{ = }(4)/(-4+4) \\ m(CD)\text{ = }(4)/(0) \\ m(CD)\text{ = }\infty \end{gathered}`

A line that has an infinite slope is a vertical line

For the two lines to be parallel, m(AB) should be equal to m(CD)

For the two lines to be perpendicular, m(AB) = -1 / m(CD)

None of the conditions for paralleleism and perpendicularity is met, the lines AB and CD are neither parallel nor perpendicular