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Math Help - Little League Baseball

  1. #1
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    Little League Baseball

    The layout of a Little League playing field is a square, 60 feet on a side.
    Overlay a rectangular coordinate system on a Little League baseball diamond so that the orgin is at home plate, the positve x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

    (a) What are the coordinates of first base, second base and third base? (Use feet as unit of measurement.)

    (b) If the right fielder is located at point (180, 20), how far is it from there to second base?

    (c) If the center fielder is located at point (220, 220), how far is it from there to third base?
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  2. #2
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    Quote Originally Posted by symmetry View Post
    The layout of a Little League playing field is a square, 60 feet on a side.
    Overlay a rectangular coordinate system on a Little League baseball diamond so that the orgin is at home plate, the positve x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

    (a) What are the coordinates of first base, second base and third base? (Use feet as unit of measurement.)
    Draw a picture- pictures always help, especially later in Mathematics.

    Note: units in feet

    Obviously home is (0,0), the origin of the graph.

    first base: (60, 0)
    2nd base: (60, 60)
    3rd base: (0, 60)
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  3. #3
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    Quote Originally Posted by symmetry View Post
    The layout of a Little League playing field is a square, 60 feet on a side.
    Overlay a rectangular coordinate system on a Little League baseball diamond so that the orgin is at home plate, the positve x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

    (b) If the right fielder is located at point (180, 20), how far is it from there to second base?
    A couple of ways to do this. One way is to use the distance formula.

    (We know 2nd base is at (60, 60); the right fielder is at (180, 20);

    d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2)

    d = sqrt((180 - 60)^2 + (20 - 60)^2)

    = sqrt ((120)^2 + (-40)^2)

    = sqrt(16,000)

    = 40*sqrt(10)

    Which is about 126.5 feet.
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  4. #4
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    Quote Originally Posted by symmetry View Post
    The layout of a Little League playing field is a square, 60 feet on a side.
    Overlay a rectangular coordinate system on a Little League baseball diamond so that the orgin is at home plate, the positve x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base.

    (c) If the center fielder is located at point (220, 220), how far is it from there to third base?
    Same deal as part b;

    We know 3rd base is located at (0, 60);

    Use the distance formula again. You should be able to easily plug in the values and figure it out.

    You should get 20*sqrt(185) or roughly 272.03 feet.
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  5. #5
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    ok

    Wow! I did not realize how easy this question truly is.

    Thanks.
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