Answer:
If the lines BC and DE are parallel, the value of c is c=-2
Step-by-step explanation:
We are given line segment BC with end points B(2, 2) and C(9,6) and line segment DE with endpoints D(c, -7) and E(5, -3).
Using slope formula: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex] we can find point c
When 2 lines are parallel there slope is same.
So, Slope of line BC =Slope of Line DE
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have:
[tex]x_1=2, y_1=2, x_2=9, y_2=6 \ for \ line \ BC \ and \\\x_1=c, y_1=-7, x_2=5, y_2=-3 \ for \ line \ DE \[/tex]
Putting values and finding c
[tex]\frac{6-2}{9-2}=\frac{-3-(-7)}{5-c}\\ \frac{4}{7}=\frac{-3+7}{5-c} \\ \frac{4}{7}=\frac{4}{5-c} \\Cross \ multiply:\\4(5-c)=4*7\\20-4c=28\\-4c=28-20\\-4c=8\\c=\frac{8}{-4}\\c=-2[/tex]
So, If the lines BC and DE are parallel, the value of c is c=-2
