Question

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

Answer 1

x=-6

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=(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=(4-14)/(-2+6)`

`m_E_F=(-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=(-4-16)/(2-x)`

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

Remember that

`m_C_D=m_E_F`

so

`(-20)/(2-x)=-2.5`

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