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=}(-9-(-1))/(6-(-6)) \\ =(-9+1)/(12) \\ =-(8)/(12) \\ =-(2)/(3) \end{gathered}`

Point C is at (3,2).

`\begin{gathered} -(2)/(3)=(2-y)/(3-x) \\ \text{If y=4,x=0} \\ (2-4)/(3-0)=-(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}=(-8-2)/(18-3) \\ =-(10)/(15) \\ =-(2)/(3) \end{gathered}`

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