Question

Line AB formed by (2,3) and (-1,4)Line CD formed by (-5,3) and (-4,6)Parallel perpendicular or neither

Answer 1

To check whether the lines are perpendicular or parallel, we will use the following rules:

1) For parallel lines, the slopes are equal.

2) For perpendicular lines, the product of the slopes is equal to -1.

Slope of line AB:

Using

`\begin{gathered} (x_1,y_1)=(2,3) \\ (x_2,y_2)=(-1,4) \end{gathered}`

The slope is given as

`\begin{gathered} m_A=(y_2-y_1)/(x_2-x_1) \\ m_A=(4-3)/(-1-2) \\ m_A=-(1)/(3) \end{gathered}`

Slope of line CD:

Using

`\begin{gathered} (x_1,y_1)=(-5,3) \\ (x_2,y_2)=(-4,6) \end{gathered}`

The slope is given as

`\begin{gathered} m_B=(y_2-y_1)/(x_2-x_1) \\ m_B=(6-3)/(-4-(-5)) \\ m_B=(3)/(-4+5) \\ m_B=3 \end{gathered}`

Comparing both slopes, we can observe that

`\begin{gathered} m_A* m_B=-1 \\ \text{Given that} \\ -(1)/(3)*3=-1 \end{gathered}`

Therefore, both lines are PERPENDICULAR.