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Math Help - Find the other end of the diameter

  1. #1
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    Find the other end of the diameter

    A circle with the center at (5,1) has a diameter that terminates at (6,3) . Find the other end of the diameter.

    This is the formula of finding the center of two point

    x=1/2(x1+x2)
    y=1/2(y1+y2)

    but what if the center is given and you have to find the other end,.,what is the formula?
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  2. #2
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    Quote Originally Posted by jasonlewiz View Post
    A circle with the center at (5,1) has a diameter that terminates at (6,3) . Find the other end of the diameter.

    This is the formula of finding the center of two point

    x=1/2(x1+x2)
    y=1/2(y1+y2)

    but what if the center is given and you have to find the other end,.,what is the formula?
    1. Let C(x_C, y_C) the midpoint of a line segment (in your case it is a diameter). Then your formula becomes:

    \begin{array}{l}x_C=\frac12(x_1+x_2) \\y_C=\frac12(y_1+y_2)\end{array}

    2. You must know the coordinates of 2 points to calculate the coordinates of the third one. For instance: If you know the coordinates of the midpoint and the coordinates of P(x_1, y_1) then you have to solve the equations for x_2 respectively for y_2
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    -deleted post-
    Last edited by ukorov; November 15th 2009 at 04:07 AM.
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  4. #4
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    Quote Originally Posted by jasonlewiz View Post
    A circle with the center at (5,1) has a diameter that terminates at (6,3) . Find the other end of the diameter.

    This is the formula of finding the center of two point

    x=1/2(x1+x2)
    y=1/2(y1+y2)

    but what if the center is given and you have to find the other end,.,what is the formula?
    for x coordinate of the other end:
    5 = \frac{x + 6}{2}
    for y-coordinate of the other end:
    1 = \frac{y + 3}{2}
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  5. #5
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    Hello, jasonlewiz!

    A circle with the center at C(5,1) has a diameter that terminates at A(6,3).
    Find the other end of the diameter.
    Did you make a sketch? . . . The answer will be obvious.

    Code:
          |               A
          |               o
          |               ↑
          |               ↑2
          |         C     ↑
          |   + ← ← o → → +
          |   ↓        1
        --+---↓-----+----------
          |   ↓     5
          |   o
          |   B

    To get from the center C(5,1) to point A(6,3),
    . . we move 1 unit right and 2 units up.

    Hence, to get the other end of the diameter B,
    . . we start at C and move 1 unit left and 2 units down.

    Got it?

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