Question

Given B(17, 5), C(11, -3), D(-1, 2), and E(x, -6), find the value of x so that BC is parallel to DE

Answer 1

First we need to find the equation of the line BC

B (17,5)=(x1,y1)

C(11,-3)=(x2,y2)

First we need to find the slope

`m=(y_2-y_1)/(x_2-x_1)`
`m=(-3-5)/(11-17)=(-8)/(-6)=(4)/(3)`

Because DE is parallel to BC they have the same slope

D(-1,2)=(x1,y1)

E(x,-6)=(x2,y2)

`m=(4)/(3)=(-6-2)/(x+1)=(-8)/(x+1)`

`(4)/(3)=(-8)/(x+1)`
`((x+1)4)/(3)=-8`
`(4x+4)/(3)=-8`
`4x+4=-8(3)`
`4x+4=-24`
`4x=-24-4`
`4x=-28`
`x=(-28)/(4)=-7`

x=-7