Question

on the diagram below draw a line that passes through point C and is parrallel to AB. explain how you created your line.If the line you drew in #2 was extended, would it eventually pass through the point E(18,-8)? Explain how you determined your yes/no answer.

Answer 1

To create the line, first, recall the definition of parallel lines.

Two lines are parallel if they have the same slope.

First, calculate the slope of line AB with A(-6,-1) and B(6,-9).

$\begin{gathered} \text{Slope of AB=}\frac{-9-(-1)}{6-(-6)} \\ =\frac{-9+1}{12} \\ =-\frac{8}{12} \\ =-\frac{2}{3} \end{gathered}$

Point C is at (3,2).

$\begin{gathered} -\frac{2}{3}=\frac{2-y}{3-x} \\ \text{If y=4,x=0} \\ \frac{2-4}{3-0}=-\frac{2}{3} \\ \implies D(0,4) \end{gathered}$

Draw a line to D(0,4) to create a parallel line.

If the line was extended, to determine if it passes through (18,-8), pick points C and (18,-8) and check if its slope is -2/3.

C(3,2) and (18,-8).

$\begin{gathered} \text{Slope}=\frac{-8-2}{18-3} \\ =-\frac{10}{15} \\ =-\frac{2}{3} \end{gathered}$

Since the slope is -2/3, it passes through the point (18,-8).