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Math Help - Diagonal distance does not add up?

  1. #1
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    Diagonal distance does not add up?

    The first quadrant of the circle has a radius of 20 units.

    At 90 degrees y runs from 1 to 20 down

    At circle centre x run from 1 to 20

    so origin is 1,20

    now place an X in position 12,6

    now determine the diagonal distance :

    d = sqrt ( (12-1)*(12-1) + (6-20)*(6-20) )

    d = sqrt ( 317 )

    d = 18 (rounded)

    but X is 19 diagonal units?

    Try another :

    place an X in position 10,11

    d = sqrt ( (10-1)*(10-1) + ( 11-20)*(11-20) )

    d = sqrt (162)

    d = 13 (rounded) this is correct

    Try another one for a wrong answer:

    place an X in position 19,20

    d = sqrt ( (19-1)*(19-1) + (20-20)*(20-20) )

    d = sqrt (324)

    d = 18

    I lost and have been doing the math all day and do not see where I am making a cock up!

    Help please?

    Thanks
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  2. #2
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    Quote Originally Posted by freddie View Post
    The first quadrant of the circle has a radius of 20 units.

    At 90 degrees y runs from 1 to 20 down

    At circle centre x run from 1 to 20

    so origin is 1,20
    I would interpret this as saying that the center is at (21/2, 21/2) and the radius is 21/2- 1= 19/2 or 20- 21/2= 19/2.
    Or are you saying that the center is at (1, 1) and (20,1) and (1, 20) are on the circle? In that case the radius is 19 units.

    now place an X in position 12,6

    now determine the diagonal distance :

    d = sqrt ( (12-1)*(12-1) + (6-20)*(6-20) )

    d = sqrt ( 317 )

    d = 18 (rounded)

    but X is 19 diagonal units?
    So? You didn't say that X was a point on the circle. Did you intend that?

    Try another :

    place an X in position 10,11

    d = sqrt ( (10-1)*(10-1) + ( 11-20)*(11-20) )

    d = sqrt (162)

    d = 13 (rounded) this is correct

    Try another one for a wrong answer:

    place an X in position 19,20

    d = sqrt ( (19-1)*(19-1) + (20-20)*(20-20) )

    d = sqrt (324)

    d = 18
    Why is that wrong? What are you trying to do?

    I lost and have been doing the math all day and do not see where I am making a cock up!

    Help please?

    Thanks
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  3. #3
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    Hi,

    Ok so I have some graph paper and have a vertical line 20 squares long, these are numbered 1 to 20

    Then from square 20 I have 20 squares on the horizontal numbered 1 to 20

    So I have the radios starting on the x axis starting at 1

    I have an arc going from the ends of each line

    So if I place an X on the x axis at 19,20 should not the distance calculation equal 19 and not 18?

    Afterall other calculations hit the X spot on?
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  4. #4
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    Quote Originally Posted by freddie View Post
    Hi,

    Ok so I have some graph paper and have a vertical line 20 squares long, these are numbered 1 to 20

    Then from square 20 I have 20 squares on the horizontal numbered 1 to 20

    So I have the radios starting on the x axis starting at 1

    I have an arc going from the ends of each line

    So if I place an X on the x axis at 19,20 should not the distance calculation equal 19 and not 18?

    Afterall other calculations hit the X spot on?
    You said you have the squares numbered 1 to 20. What about points on the line? How are they numbered? And what in the world do you mean by "X on the x axis at 19,20"? Do you mean the X is at the line between the squares labeled 19 and 20? Then, yes, the distance from the start of the "x-axis" to that point is 19.

    However, if you are referring to what you said before:
    "place an X in position 19,20
    d = sqrt ( (19-1)*(19-1) + (20-20)*(20-20) )"
    (but that point is NOT "on the x axis".)

    so that the X is covering the square labeled 19 horizontally and 20 vertically, then 2 things:
    1) that is not a point- it is an entire square.
    2) If you mean the point at distance 19 horizontally from the beginning of the horizontal line and 20 vertically from that line, then its distance from the beginning of the horizontal line is [itex]\sqrt{19^2+ 20^2}[/itex] which is NOT 19.

    I think you may be confusing yourself (certainly me!) by labeling squares rather than points.
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  5. #5
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    OK so before replying I have spent much time drawing a circle on graph paper using the lines as the points and NOT the squares.

    After plotting and plotting I can now thankfully say I get it.

    So I can now accurately calculate the distances and the degrees too, thank to you pointing out my error

    Thanks a million!
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