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Thread: Finding the coordinates of a point

  1. #1
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    Finding the coordinates of a point

    I am given a point P(x1,y1). I have to find the coordinates of a point at
    a distance say DIS from it. The only thing we are given is that this
    point maintains the angles XO,YO with the x ,y axis respectively. I told
    my boss that I am having trouble with this but he said that it is
    supposed to be simple and that I have all the information I need. I always
    used to consider myself a good math student until today (completed my
    education and always got good grades in Math). But now I am starting to
    doubt my math capability! Please help me figure out how to do this. Its actually in 3 dimensions but I figured it would be
    easy to do this in 2D first. How do we find the coordinates of the
    point A?

    /A(x,y?)
    /
    DIS /
    /
    /
    /XO
    /________________________x axis
    P( x1,y1)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mathasker
    I am given a point P(x1,y1). I have to find the coordinates of a point at
    a distance say DIS from it. The only thing we are given is that this
    point maintains the angles XO,YO with the x ,y axis respectively. I told
    my boss that I am having trouble with this but he said that it is
    supposed to be simple and that I have all the information I need. I always
    used to consider myself a good math student until today (completed my
    education and always got good grades in Math). But now I am starting to
    doubt my math capability! Please help me figure out how to do this. Its actually in 3 dimensions but I figured it would be
    easy to do this in 2D first. How do we find the coordinates of the
    point A?

    /A(x,y?)
    /
    DIS /
    /
    /
    /XO
    /________________________x axis
    P( x1,y1)

    The points $\displaystyle DIS$ from $\displaystyle A(u,v)$ define a circle with equation:

    $\displaystyle (x-u)^2+(x-v)^2=DIS^2$

    The condition that the line $\displaystyle PA$ make an angle $\displaystyle XO$ with the
    x-axis is that the line $\displaystyle PA$ has slope $\displaystyle \tan (XO)$. So
    now find the equation of a line of slope $\displaystyle \tan(XO)$ which passes
    through $\displaystyle A(u,v)$, and then solve for the points of intersection of
    this line with the circle.

    RonL
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  3. #3
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by Mathasker
    I am given a point P(x1,y1). I have to find the coordinates of a point at
    a distance say DIS from it. The only thing we are given is that this
    point maintains the angles XO,YO with the x ,y axis respectively. I told
    my boss that I am having trouble with this but he said that it is
    supposed to be simple and that I have all the information I need. I always
    used to consider myself a good math student until today (completed my
    education and always got good grades in Math). But now I am starting to
    doubt my math capability! Please help me figure out how to do this. Its actually in 3 dimensions but I figured it would be
    easy to do this in 2D first. How do we find the coordinates of the
    point A?

    /A(x,y?)
    /
    DIS /
    /
    /
    /XO
    /________________________x axis
    P( x1,y1)
    See if I understand your question:
    ---line segment DIS is DIS long. [ :-) ].
    ---top endpoint of DIS is A(x,y)
    ---bottom endpoint of DIS is P(x1,y1)
    ---angle included by DIS and a horizontal line is XO
    ---point P is not on the x-axis. Otherwise, if it is, then y1 = 0.
    ---you like to solve for the x and y of point A

    If I got the question, then:
    x = x1 +(DIS)*cos(X0)
    y = y1 +(DIS)*sin(X0)
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