Question

Does anyone know how to solve this?

Answer 1

x = - 6

Explanation:

Parallel lines have equal slopes

Calculate the slopes of EF and CD and equate them

Calculate slopes using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = E (- 6, 14 ) and F (- 2, 4 )

`m_(EF)` =
`(4-14)/(-2-(-6))` =
`(-10)/(-2+6)` =
`(-10)/(4)` = -
`(5)/(2)`

Repeat with (x₁, y₁ ) = C (x, 16 ) and (x₂, y₂ ) = D (2, - 4 )

`m_(CD)` =
`(-4-16)/(2-x)` =
`(-20)/(2-x)`

Equate the 2 slopes and solve for x

`(-20)/(2-x)` =
`(5)/(-2)` ( 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