197k views
5 votes
Given B(17,5), C(11, -3), D-1, 2), and
E(x, -6), find the value of x so that BC || DE.

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

1 Answer

3 votes

Answer:


x=-7

Explanation:

Remember that:

  • Two lines are parallel if their slopes are the same.
  • Two lines are perpendicular if their slopes are negative reciprocals.
  • And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.

We want to find the value of x such that
\overline{BC}\parallel\overline{DE}.

Therefore, the slopes of BC and DE must be equivalent.

So, let's find the slope of BC first.

BC)

We can use the slope formula:


\displaystyle m=(y_2-y_1)/(x_2-x_1)

Let B(17, 5) be (x₁, y₁) and let C(11, -3) be (x₂, y₂). Substitute:


\displaystyle m=(-3-5)/(11-17)

Subtract:


m=-8/-6=4/3

So, the slope of BC is 4/3.

DE)

Let D(-1, 2) be (x₁, y₁) and let E(x, -6) be (x, y₂). Substitute:


\displaystyle m=(-6-2)/(x-(-1))

We know that the two slopes must be equal. So, the slope of DE must also be 4/3. Substitute 4/3 for m:


\displaystyle (4)/(3)=(-6-2)/(x-(-1))

Solve for x. Simplify the right:


\displaystyle (4)/(3)=(-8)/(x+1)

Cross multiply:


4(x+1)=-8(3)

Multiply on the right:


4(x+1)=-24

Divide both sides by 4:


x+1=-6

Subtract 1 from both sides:


x=-7

So, the value of x is -7.

And we're done!

User Yuyang
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories