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.

Answer 1

Solving this problem actually requires us the use of the distance formula of point to a line.

The formula is:

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

 

So we are given the equation:

y = 2 x + 4

rewriting:

y – 2 x – 4 = 0     --> a = -2, b = 1, c = -4

 

We are also given the points:

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

 

Using the distance formula at points (x, y):

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

distance = 15 / sqrt (5)

distance = 6.7

 

So the tree is about 6.7 ft away from the zip line.