Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

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

Sagot :

sqdancefan

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

View image sqdancefan
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.