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Find the distance between the point (6.3) and the line 3x + 5y +1=0.

User Eyllanesc
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1 Answer

22 votes
22 votes

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Answer:

√34 ≈ 5.831

Explanation:

The distance (d) between point (x, y) and the line ax +by +c = 0 is given by ...

d = |ax +by +c|/√(a²+b²)

Using the given values, the distance is ...

d = |3(6) +5(3) +1|/√(3² +5²) = 34/√34

d = √34

The distance between the point and the line is √34 ≈ 5.831 units.

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The graph confirms this result by showing the line is tangent to a circle with radius √34 centered on (6, 3).

Find the distance between the point (6.3) and the line 3x + 5y +1=0.-example-1
User Tomasz Onyszko
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3.1k points