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}\\m_E_F=\frac{-10}{4}\\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}\\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]
Parallel lines have the same slope
The value of x is -6
The coordinates of the points are:
[tex]\mathbf{C = (x,16)}[/tex]
[tex]\mathbf{D = (2,-4)}[/tex]
[tex]\mathbf{E = (-6,14)}[/tex]
[tex]\mathbf{F = (-2,4)}[/tex]
Calculate the slope of CD using:
[tex]\mathbf{m = \frac{y_2 - y_2}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{CD = \frac{-4 - 16}{2 - x}}[/tex]
[tex]\mathbf{CD = \frac{-20}{2 - x}}[/tex]
Calculate the slope of EF using the same slope formula
[tex]\mathbf{EF = \frac{4 - 14}{-2 - -6}}[/tex]
[tex]\mathbf{EF = \frac{- 10}{4}}[/tex]
Because both lines are parallel, then:
[tex]\mathbf{CD = EF}[/tex]
So, we have:
[tex]\mathbf{\frac{-20}{2 - x} = \frac{- 10}{4}}[/tex]
Divide both sides by -10
[tex]\mathbf{\frac{2}{2 - x} = \frac{1}{4}}[/tex]
Cross multiply
[tex]\mathbf{2-x = 8}[/tex]
Solve for x
[tex]\mathbf{x = 2 - 8}[/tex]
[tex]\mathbf{x = - 6}[/tex]
Hence, the value of x is -6
Read more about slopes of parallel lines at:
https://brainly.com/question/12203383
