Answer:
x = - 6
Step-by-step explanation:
Parallel lines have equal slopes
Calculate the slopes of EF and CD and equate them
Calculate slopes using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } [/tex]
with (x₁, y₁ ) = E (- 6, 14 ) and F (- 2, 4 )
[tex]m_{EF} [/tex] = [tex]\frac{4-14}{-2-(-6)} [/tex] = [tex]\frac{-10}{-2+6} [/tex] = [tex]\frac{-10}{4} [/tex] = - [tex]\frac{5}{2} [/tex]
Repeat with (x₁, y₁ ) = C (x, 16 ) and (x₂, y₂ ) = D (2, - 4 )
[tex]m_{CD} [/tex] = [tex]\frac{-4-16}{2-x} [/tex] = [tex]\frac{-20}{2-x} [/tex]
Equate the 2 slopes and solve for x
[tex]\frac{-20}{2-x} [/tex] = [tex]\frac{5}{-2} [/tex] ( cross- multiply )
5(2 - x) = 40 ( divide both sides by 5 )
2 - x = 8 ( subtract 2 from both sides )
- x = 6 ( multiply both sides by - 1 )
x = - 6
