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Math Help - Calculate points on a line

  1. #1
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    Calculate points on a line

    Hi,

    How can I calculate all the points on a diagonal line if I only know the x/y coordinates of 2 fixed points.

    See the picture, only 2 points are known (the x/y coordinate) and I want to know the other 3 points on the line. And lets say the distance/space between each point is 1cm.

    Calculate points on a line-points.png

    Thanks.
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  2. #2
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    Re: Calculate points on a line

    Hi Fri I'm don't know well in English but I know how to solve it.first we have to find third by ((2+4)/2;(1+5)/2) then find second point like before
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  3. #3
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    Re: Calculate points on a line

    Isn't there a way to get each point by incrementing it by 1cm?
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  4. #4
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    Re: Calculate points on a line

    Quote Originally Posted by mplus View Post
    Hi,

    How can I calculate all the points on a diagonal line if I only know the x/y coordinates of 2 fixed points.

    See the picture, only 2 points are known (the x/y coordinate) and I want to know the other 3 points on the line. And lets say the distance/space between each point is 1cm.

    Click image for larger version. 

Name:	points.PNG 
Views:	3 
Size:	1.5 KB 
ID:	24318
    write the equation for the line ...

    m = \frac{5-1}{4-2} = 2

    y - 1 = 2(x - 2)

    y = 2x - 3

    evaluate y for the x values you desire between 2 and 4
    Thanks from HallsofIvy
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  5. #5
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    Re: Calculate points on a line

    Quote Originally Posted by mplus View Post
    Hi,

    How can I calculate all the points on a diagonal line if I only know the x/y coordinates of 2 fixed points.

    See the picture, only 2 points are known (the x/y coordinate) and I want to know the other 3 points on the line. And lets say the distance/space between each point is 1cm.
    So you have a total of five points, including the endpoints, and the distance between tonsecutive points is 1 cm?
    That's impossible- the length of the line is \sqrt{(4- 2)^2+ (5-1)^2}= \sqrt{4+1}= \sqrt{5}, not 4 as it would have to be to have 1 cm between them. If you simply mean "3 points equally distribute between (2, 1) and (4, 5)", then they must have distance \frac{\sqrt{5}}{4}} between them. Also the slope of the line is (5- 1)/(4- 2)= 4/2= 2. The first point (the one closest to (2, 1)), must satisfy \sqrt{(x- 1)^2+ (y- 2)^2}= \frac{\sqrt{5}}{2} or (x-1)^2+ (y-2)^2= \frac{5}{4} and \frac{y- 1}{x- 2}= 2 or y-1= 2(x-2). The second must satisfy \sqrt{(x- 1)^2+ (y- 2)^2}= 2\frac{\sqrt{5}}{2} or (x-1)^2+ (y-2)^2= 5 as well as y- 1= 2(x- 2). The third must satisfy \sqrt{(x- 1)^2+ (y- 2)^2}= 3\frac{\sqrt{5}}{2} or (x-1)^2+ (y-2)^2= \frac{45}{4} and y-1= 2(x- 2).

    Click image for larger version. 

Name:	points.PNG 
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ID:	24318

    Thanks.
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  6. #6
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    Re: Calculate points on a line

    No the total distance from point 1 to 5 isn't 1cm. Its supposed to be 4.46cm. I mean to get the 3 points increased by 1.18cm to end up with 3 points. And get the xy coordinate of those 3 points.

    So yes the idea is to get the coordinate of 3 points equally distributed between the 2 known coordinates yes.

    I didn't really get the math part you wrote at the second paragraph.

    You said the second points, so the one in the middle, is 5? I want its x y coordinate.

    I didn't get this part either:

    y = 2x - 3

    evaluate y for the x values you desire between 2 and 4
    Last edited by mplus; July 20th 2012 at 08:34 AM.
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  7. #7
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    Re: Calculate points on a line

    if you evenly divide the interval from x = 2 to x = 4 into four equal parts, you get the x-values 2, 2.5, 3, 3.5 and 4

    the evenly spaced coordinates would be

    (2 , 1)

    (2.5 , 2)

    (3 , 3)

    (3.5 , 4)

    (4 , 5)

    if you do not know how to write a linear equation between two points, then I recommend you visit this link and study the lesson ...

    Straight-Line Equations: Slope-Intercept Form
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  8. #8
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    Re: Calculate points on a line

    Hello, mplus!

    How can I calculate the points on a diagonal line if I only know the x/y coordinates of 2 fixed points.

    See the picture, only 2 points are known (the x/y coordinate) and I want to know the other 3 points on the line. And lets say the distance/space between each point is 1cm.

    Click image for larger version. 

Name:	points.PNG 
Views:	3 
Size:	1.5 KB 
ID:	24318

    Look at what we have:

    . . \begin{array}{ccccccccccc} (2,1)\;\bullet &--& \bullet &--& \bullet &--& \bullet &--& \bullet \;(4,5) \end{array}


    We want to divide the line segment into four equal segments.

    The x-coordinates range from 2 to 4.
    . . Hence, the x-coordinates are: . 2,\,2\tfrac{1}{2},\,3,\,3\tfrac{1}{2},\,4

    The y-coordinates range from 1 to 5.
    . . Hence, the y-coordinates are: . 1,\,2,\,3,\,4,\,5.


    Therefore, the five points are: . (2,\,1),\:\left(\tfrac{5}{2},\,2\right),\:(3,\,3),  \:\left(\tfrac{7}{2},\,4\right),\:(4,\,5)


    Ah ... skeeter beat me to it . . .
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  9. #9
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    Re: Calculate points on a line

    Ah thanks, that did it.
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