Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

shivam_bhalla

  • 2 years ago

For Points P=(x_1,y_1) and Q(x_2,y_2) of the coordinate plane a new distance d(P,Q) is defined by d(P,Q) = |x_1 - x_2|+|y_1-y_2| Let O = (0,0) and A = (3,2). Prove that the set of points in the first quadrant which are equidistant (with respect to the new distance) from O and A consists of the union of a line segment of finite length and an infinite ray . Sketch this set in a labelled diagram. (10 marks)

  • This Question is Closed
  1. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The hardest part of this question is the language :/

  2. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I swear :P

  3. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    using the new distance definition, then for some point (x,y) setting the distance equal to both O and A \[\rightarrow |x| +|y| = |x-3| +|y-2|\] now to show that is a union of line segment and ray ...

  4. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    hmm not a fan of absolute value functions

  5. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |x| + |y| = |x-3| + |y-2| Since it's the first quadrant, x and y shall be positive. x + y = |x-3| + |y-2| Now up till (2,2) The line should be x+y = -x + 3 - y + 2 2x + 2y = 5

  6. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Is this right?

  7. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes. It is right. But I am facing the problem in understanding this question.

  8. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Ishaan94 and @dumbcow , how would you proceed further??

  9. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm they (the question) have defined a new distance formula.

  10. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1335436017723:dw|And we are supposed to get the points which are equidistant from the points O and A, using the new distance formula. Is that right? @dumbcow

  11. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    correct

  12. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It should be the ditsnace individually. Suppose. See the dig below|dw:1335436193825:dw| Like distance between O and P (by new distance formula) should be equal to distance between A and Q (by new distance formula)

  13. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    *distance

  14. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I can't get the line after (3,2) x + y = x-3 + y-2 Hmm are you sure the equation is correct? @shivam_bhalla

  15. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It is a question from IITJEE .

  16. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it seems that no points outside (3,2) are equidistant to O and A

  17. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Hmm but the result can't lie. Maybe you could check the equation again? because the question says an infinite ray and finite distance, and we didn't get the infinite one.

  18. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The question is correct. I have referred from 2 books. It is a math question from IITJEE year 2000 (main)

  19. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Let me check.

  20. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    See here. Question 4 ->http://www.askiitians.com/iit-papers/IIT-JEE-2000-mathematics-mains.aspx

  21. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Strange the question is right http://www.askiitians.com/iit-papers/IIT-JEE-2000-mathematics-mains.aspx

  22. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I have the 30 years, I will be back in a moment.

  23. dumbcow
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    http://www.wolframalpha.com/input/?i=abs%28x%29%2Babs%28y%29+%3D+abs%28x-3%29%2Babs%28y-2%29 looks like we forgot the case where y>2 but x<3 --> x = 1/2

  24. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh yeah

  25. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :-/ and I was trying to blame the question

  26. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wish I have wolfram alpha with me in my exams. Thanks @Ishaan94 and @dumbcow for the help. I wish had 2 medals to give away

  27. Ishaan94
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lol, with enough practice you won't need wolfram. goodluck. :-)

  28. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks :D

  29. eliassaab
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Study the 9 regions defined by the lines in the attacehd file, each one separtely. It would be easy to get rid the absloute sign. For eaxmple the bounded region we have \[ 0\le x \le 3\\ 0\le y \le 2 \] In this region we 3 - x + 2 -y = x + y 2 x + 2y = 5 y= -x + 5/2 Study the othe regions and see what you can get.

    1 Attachment
  30. shivam_bhalla
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @eliassaab , Thanks for your help. I had initially problem in understanding the question. But I am comfortable with modulus function, just that my brain had gone blank at that time after reading the question :)

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

    • 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.