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3 years ago

What is the distance between 3x - 5y + 3 =0 and 6x - 10y -12 =0

Mathematics

1 answer:

pogonyaev3 years ago

5 0

9514 1404 393

Answer:

(9/34)√34 ≈ 1.543

Step-by-step explanation:

The second equation can be rewritten as ...

6x -10y -12 = 0

3x -5y -6 = 0

3x -5y = 6

The formula for the distance from point (x, y) to line ax+by+c=0 is ...

d = |ax+by+c|/√(a²+b²)

Then the distance from a point to the first line is ...

d = |3x -5y +3|/√(3² +(-5)²)

We know from the rearrangement of the second equation that points on its line satisfy (3x-5y) = 6. Substituting this value for (3x -5y) in the distance formula gives ...

d = |6 +3|/√34

Simplifying and rationalizing the denominator gives a distance of ...

d = (9/34)√34 ≈ 1.543

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