Question

You are setting up a zip line in your yard. You map out your yard in a coordinate plane. An equation of the line representing the zip line is y=2x+4. There is a tree in your yard at the point (−4, 11). Each unit in the coordinate plane represents 1 foot. Approximately how far away is the tree from the zip line? Round your answer to the nearest tenth.

Answer 1

Answer:

Distance is 6.7units to the nearest tenth.

Explanation:

To solve this problem, we the distance formula. And this is given as:

$D = \frac{|a x + b y + c|}{\sqrt{a^2 + b^2}}$

We were given the equation:

y = 2 x + 4

This can also be rewritten as:

y – 2 x – 4 = 0.

Therefore, a = -2, b = 1 and c = -4

Also, we were given the points:

(x, y) = (–4, 11)

Making use of the above formula for distance, we have:

$D = \frac{|-2\times -4 + 1\times 11 + -4|}{\sqrt{-2^2 + -4^2}}$

$D = \frac{15}{\sqrt{5}}$

D = 6.7units (to the nearest tenth)