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Math Help - Need help with right bisector/circle questions

  1. #1
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    Need help with right bisector/circle questions

    I'll write out what I need help with.

    The endpoints of a line segment are A(-7,-1) and B(5,5).

    a) Determine the equation of the right bisector of AB.

    I have AB's midpoint as (-1,2), AB's slope as 1/2, and the slope of the right bisector as -2.

    y-2=-2(x-(-1))
    y-2=-2x-2
    y=-2x-2+2
    y=-2x

    Therefore the equation of the right bisector of AB is y=-2x

    I'm not sure if that's correct. Could someone look it over and see if I made any mistakes?

    I also need help with two more questions;

    b) Show that the origin, (0,0), lies on the right bisector of AB.
    c) Determine the equation of the circle passing through AB.

    I have no idea how to answer these questions. Can someone help me with them?
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  2. #2
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    Quote Originally Posted by mathdonkey View Post
    I'll write out what I need help with.

    The endpoints of a line segment are A(-7,-1) and B(5,5).

    a) Determine the equation of the right bisector of AB.

    I have AB's midpoint as (-1,2), AB's slope as 1/2, and the slope of the right bisector as -2.

    y-2=-2(x-(-1))
    y-2=-2x-2
    y=-2x-2+2
    y=-2x

    Therefore the equation of the right bisector of AB is y=-2x
    That's correct!

    Quote Originally Posted by mathdonkey View Post
    b) Show that the origin, (0,0), lies on the right bisector of AB.
    c) Determine the equation of the circle passing through AB.
    b) This is easy. Just verify that (0, 0) lies on y = -2x.

    c) The "circle passing through AB?" Do you mean that AB is the circle's diameter? If so then you know the center of the circle, it's your midpoint of AB. Then to find the radius find the length of the line segment between the midpoint and point A (or point B, it will be the same.) Then plug that into the equation for a circle.

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    That's correct!


    b) This is easy. Just verify that (0, 0) lies on y = -2x.
    That's the problem, I haven't been taught how to do this.

    Quote Originally Posted by topsquark
    c) The "circle passing through AB?" Do you mean that AB is the circle's diameter? If so then you know the center of the circle, it's your midpoint of AB. Then to find the radius find the length of the line segment between the midpoint and point A (or point B, it will be the same.) Then plug that into the equation for a circle.

    -Dan
    I don't know if AB is the circle's diameter. I've written the question exactly as it's written in the book, what do you think? Either way... I don't have a clue as to how I'm supposed to answer this question, the lesson in the workbook didn't teach me how to do it!
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  4. #4
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    Quote Originally Posted by mathdonkey View Post
    That's the problem, I haven't been taught how to do this.



    I don't know if AB is the circle's diameter. Mr F says: No harm done by assuming this ......

    The workbook I'm working with asks questions it hasn't taught me how to do... it's extremely frusterating.
    Quote Originally Posted by topsquark View Post
    That's correct!


    b) This is easy. Just verify that (0, 0) lies on y = -2x. Mr F says: Sub x = 0 and y = 0. Does the equation 'work'?

    c) The "circle passing through AB?" Do you mean that AB is the circle's diameter? If so then you know the center of the circle, it's your midpoint of AB. Then to find the radius find the length of the line segment between the midpoint and point A (or point B, it will be the same.) Then plug that into the equation for a circle.

    -Dan
    ..
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  5. #5
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    Quote Originally Posted by mr fantastic View Post
    Mr F says: Sub x = 0 and y = 0. Does the equation 'work'?
    I don't know what that means.
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  6. #6
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    Quote Originally Posted by mathdonkey View Post
    I don't know what that means.
    The equation is y = -2x. You want to verify that the point (0, 0) lies on it.

    The point (0, 0) corresponds to x = 0 and y = 0.

    So you want to verify that x = 0 and y = 0 satisfies y = -2x.

    Substitute: 0 = -2(0) therefore 0 = 0. Is this a true statement? So does x = 0 and y = 0 satisfy y = -2x ?

    Or, in my own way of trying to cut to the chase, does the equation 'work' when you sub x = 0 and y = 0.

    By the way, don't take offense at this, but I'm astounded that you would be working on a question like this and NOT know how to verify that a given point lies on a line ......
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  7. #7
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    Quote Originally Posted by mr fantastic View Post
    By the way, don't take offense at this, but I'm astounded that you would be working on a question like this and NOT know how to verify that a given point lies on a line ......
    Don't worry about it, it frustrates me too. I dropped out of high school a year and a half ago and now I'm doing independant study to get the credits (and marks) I need for university. The workbooks I've been given for it are ridiculous though. They ask questions they haven't prepared me for, and my marks depend on me coming up with the answers on my own. Not to mention I've found actual errors in the lessons they have written in the books. I'm not talking about spelling errors, I mean actual errors in the methods they teach. It's taking a huge toll on my confidence, but working through it is my only option...

    And yes, if both y and x are 0, then y=-2x is correct.

    Thanks for explaining that to me! Is there anything else I need to know for this, like a specific way for writing my answer?
    Last edited by mathdonkey; January 27th 2008 at 09:50 PM.
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