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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=−4/5x+5. There is a tree in your yard at the point (4, 10). 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.

User Mouser
by
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1 Answer

3 votes

Answer:

The tree is approximately 6.4 feet away from the zip line.

Explanation:

Equation of the line representing the zip line is
y=-(4)/(5)x+5

First we need to convert the above equation into
ax+by+c=0 form. So........


y=-(4)/(5)x+5\\ \\ 5y=5(-(4)/(5)x+5)\\ \\ 5y=-4x+25\\ \\ 4x+5y-25=0

Thus,
a=4, b=5 and
c=-25

The formula for distance
(d) from a point
(x_(0), y_(0)) to the line
ax+by+c=0 is.........


d=(|a(x_(0))+b(y_(0))+c|)/(√(a^2+b^2))

Given that, there is a tree in your yard at the point (4, 10). So here,
x_(0)=4 and
y_(0)=10

Thus, the distance will be:
d=(|4(4)+5(10)-25|)/(√(4^2+5^2))= (|16+50-25|)/(√(16+25))= (41)/(√(41))=√(41)= 6.403... \approx 6.4 (Rounding to the nearest tenth)

So, the tree is approximately 6.4 feet away from the zip line.

User Luis Cazares
by
9.3k points
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