Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

LucyLu15

  • one year ago

Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10?

  • This Question is Closed
  1. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    First, find the equation of the line perpendicular to the given line that passes thorugh (2, 3). Once you have the equation of the perpendicular, solve a system of equations of the two equations to find where the lines intersect. Then, find the distance between the point of intersection and point (2, 3).

  2. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Could x=2 @mathstudent55

  3. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    could that work?

  4. Matt.Mawson
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ok this is a big pain to solve, but here it is. First put the equation of the line into y = m*x+b format y = (4/3)x + 3.333 The perpendicular line will have slope -3/4 and passes through (2,3) so it's equation will be y = (-3/4)x+4.5 The two lines intersect at (.56,4.08) The triangle with tip (.56,4.08) and right point at (2,3) has base 1.44 and height of 1.08 \[\sqrt{1.44^{2}+1.08^{2}} = 1.8 \] 1.8 is the answer

  5. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when they intersect i get (-2,6)?

  6. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What did you get for the equation of the perpendicular?

  7. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i plugged in the one that you had calculated

  8. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Matt.Mawson calculated it, but I think he made a mistake.

  9. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let's start from the beginning. The given line is: 4x + 3y = 10

  10. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solve it for y to get the slope: 3y = -4x + 10 y = (-4/3)x + 10/3

  11. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    He made a mistake right in the beginning when he subtracted the 4x from both sides. It should be -4x on the right side, but he wrote 4x.

  12. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes i get that for my equation as well. and for my perpendicular i calculated y=(3/4)x +1.5

  13. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, I have both of those.

  14. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for my point of intercept i have .88, 2.16

  15. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, I got the same x and y as you.

  16. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so how will i find the distance?

  17. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The final step is the distance between (0.88, 2.16) and (2,3)

  18. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    For that distance I get 1.4

  19. LucyLu15
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes i have that too... Okay. Thank You!

  20. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wlcm

  21. Not the answer you are looking for?
    Search for more explanations.

    Search OpenStudy
    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.