Answered

Find solutions to your questions with the help of IDNLearn.com's expert community. Join our community to receive timely and reliable responses to your questions from knowledgeable professionals.

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

Sagot :

Sqdancefanidn

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
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.