17.02.2022 the following 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+4y=2x+4. there is a tree in your yard at the point (−4, 11)(−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.

30

17.02.2022, solved by verified expert

The question is an illustration of distance between a point and a line.

The distance between the zip line and the tree is 6.70 feet

The zip line equation is given as:

The coordinates of the tree is given as:

The distance (d) between an equation and a point is:

Where:

Rewrite as

By comparison:

and

So, we have:

Evaluate square root

Remove absolute bracket

Hence, the distance between the zip line and the tree is approximately 6.70 feet

Faq

Mathematics
Solving this problem needs the distance formula of point to a line.

The formula is:

distance = | a x + b y + c | / √  (a^2 + b^2)

So we are given the equation: y = 2 x + 4

Rewriting this would be: y – 2 x – 4 = 0 ->  a = -2, b = 1, c = -4

We are also given the points:

(-4, 11) = (x, y)

Plugging it in the distance formula at points (x, y):

distance = | -2 * -4 + 1 * 11 + -4 | / √ [(- 2)^2 + (1)^2]

= 15 / √ (5)

= 6.7

So the tree is approximately 6.7 feet away from the zip line.
Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics

The answer is in the image

Mathematics