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

Step-by-step answer

17.02.2022, solved by verified expert
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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:

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 coordinates of the tree is given as:

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

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

Where:

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

Rewrite 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 as 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

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

By comparison:

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 and 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

So, we have:

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

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

Evaluate square root

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

Remove absolute bracket

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  

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

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

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Mathematics
Step-by-step answer
P Answered by PhD
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
Step-by-step answer
P Answered by PhD
The answer is in the given image

The answer is in the given image

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image