Question

Ou 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=-8/3+8

. There is a tree in your yard at the point (3,16) . 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

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Answer:

5.6 feet

Explanation:

Assuming your zip line equation is supposed to be ...

y = -8/3x +8

we can rewrite it to general form:

8/3x +y -8 = 0

8x +3y -24 = 0 . . . . multiply by 3

Now, we can use the formula for the distance from a point to a line:

d = |ax +by +c|/√(a²+b²) . . . . . distance from (x, y) to ax+by+c=0

Filling in the values we know, we have ...

d = |8(3) +3(16) -24|/√(8² +3²) = 48/√73 ≈ 5.6

The distance from the tree to the zip line is about 5.6 feet.