Question

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

Answer 1

Answer:

$x=-7$

Step-by-step 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:

$m=\frac{y_2-y_1}{x_2-x_1}$

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

$m=\frac{-3-5}{11-17}$

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:

$m=\frac{-6-2}{x-(-1)}$

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

$\frac{4}{3}=\frac{-6-2}{x-(-1)}$

Solve for x. Simplify the right:

$\frac{4}{3}=\frac{-8}{x+1}$

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!