Answer:
The value of x = -6
Step-by-step explanation:
We know that if the line CD is parallel to line EF, then their slopes will be the same.
In other words:
slope [tex]CD[/tex] = slope [tex]EF[/tex]
As we know that the slope between two points will be:
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let's find the slope of CD
as
[tex]m\:\left(CD\right)=\frac{-4-16}{2-x}[/tex]
[tex]=-\frac{20}{2-x}[/tex]
Now, let's find the slope of EF
as
[tex]m\left(EF\right)=\frac{4-14}{-2-\left(-6\right)}[/tex]
[tex]=-\frac{10}{4}[/tex]
As we already pointed out that
[tex]m\left(CD\right)=\:m\left(EF\right)[/tex]
[tex]-\frac{20}{2-x}[/tex] [tex]=-\frac{10}{4}[/tex]
[tex]-20\cdot \:4=-\left(2-x\right)\cdot \:10[/tex]
[tex]\frac{-\left(2-x\right)\cdot \:10}{-10}=\frac{-80}{-10}[/tex]
[tex]2-x=8[/tex]
[tex]x=-6[/tex]
Therefore, the value of x = -6
