Question

22. Determine the value of c so that the line

segment with endpoints B(2, 2) and C(9,6)
BC
is parallel to the line segment with endpoints
D(c, -7) and E(5, -3).

help is appreciated !!!

Answer 1

If the lines BC and DE are parallel, the value of c is c=-2

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:
`Slope=(y_2-y_1)/(x_2-x_1)` we can find point c

When 2 lines are parallel there slope is same.

So, Slope of line BC =Slope of Line DE

`(y_2-y_1)/(x_2-x_1)=(y_2-y_1)/(x_2-x_1)`

We have:

`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 \`

Putting values and finding c

`(6-2)/(9-2)=(-3-(-7))/(5-c)\\ (4)/(7)=(-3+7)/(5-c) \\ (4)/(7)=(4)/(5-c) \\Cross \ multiply:\\4(5-c)=4*7\\20-4c=28\\-4c=28-20\\-4c=8\\c=(8)/(-4)\\c=-2`

So, If the lines BC and DE are parallel, the value of c is c=-2