Question

Given C(x, 16), D(2,-4), E(-6, 14), and F(-2, 4), find the value of x so that CD || EF.

Answer 1

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

$m=\frac{y2-y1}{x2-x1}$

step 1

Find the slope EF

we have

E(-6,14) and F(-2,4)

substitute the values in the formula

$m_E_F=\frac{4-14}{-2+6}\\m_E_F=\frac{-10}{4}\\m_E_F=-2.5$

step 2

Find the slope CD

we have

C(x, 16) and D(2, -4)

substitute the values in the formula

$m_C_D=\frac{-4-16}{2-x}\\m_C_D=\frac{-20}{2-x}$

Remember that

$m_C_D=m_E_F$

so

$\frac{-20}{2-x}=-2.5$

$-20=-5+2.5x\\2.5x=-20+5\\2.5x=-15\\x=-6$