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

6.7 ft

Explanation:

For distance between point (x₁, y₁) & line ax+by+c = 0 is:

`d=\left|(ax_1+by_1+c)/(√(a^2+b^2) )\right |`

Therefore distance between point (-4, 11) & line 2x-y+4 = 0 is:

`d=\left|(2(-4)+(-1)(11)+4)/(√(2^2+(-1)^2) )\right |`

`=\left|(-8-11+4)/(√(5) )\right |`

`=6.7\ ft`