Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

akshayb Group Title

How can one test the symmetry of x axis, y axis and origin?

  • one year ago
  • one year ago

  • This Question is Open
  1. akshayb Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Please tell the answer.

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

    May I assume that you mean test some function for symmetry across the x and y axes and the origin ? :-) Generally it means applying some transformation and seeing if there is no change ie. swap x for -x and see if f(x) = f(-x) so with \[f(x) = x^{2}\]then \[f(-x)=(-x)^{2} = (-1)^{2}x^{2}= x^{2}=f(x)\]if we are plotting this function in two dimensions as \[y =x^{2}\] |dw:1359934489024:dw|then this implies symmetry of reflection across the y-axis ( pardon my drawing skills ). Symmetry across the x-axis is likewise. As regards the origin : then that is a reflection across the y-axis and then another reflection across the x-axis. Thus a circle |dw:1359935010242:dw|is symmetric across x and y axes and hence the origin too. You can deduce this from the equation for a circle, say : \[x^{2}+ y^{2} = 1\]is invariant if we swap x for -x and y for -y \[(-x)^{2} + (-y)^{2} = (-1)^{2}x^{2} + (-1)^2y^{2} = x^{2} + y^{2}\]To be complete I ought mention that reflections across the x then y axes ( or vice versa ) is equivalent to a rotation of 180 degrees around the origin ....

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

    Err, the circle was in that second graphic earlier today.

    • one year ago
  4. akshayb Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks.

    • one year ago
    • Attachments:

See more questions >>>

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.