Answer:
x=-6
Step-by-step explanation:
we know that
If two lines are parallel, then their slopes are the same
In this problem
slope CD=slope EF
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
step 1
Find the slope EF
we have
E(-6,14) and F(-2,4)
substitute the values in the formula
[tex]m_E_F=\frac{4-14}{-2+6}[/tex]
[tex]m_E_F=\frac{-10}{4}[/tex]
[tex]m_E_F=-2.5[/tex]
step 2
Find the slope CD
we have
C(x, 16) and D(2, -4)
substitute the values in the formula
[tex]m_C_D=\frac{-4-16}{2-x}[/tex]
[tex]m_C_D=\frac{-20}{2-x}[/tex]
Remember that
[tex]m_C_D=m_E_F[/tex]
so
[tex]\frac{-20}{2-x}=-2.5[/tex]
[tex]-20=-5+2.5x\\2.5x=-20+5\\2.5x=-15\\x=-6[/tex]
