Finding the coordinates of a point

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January 5th 2006, 06:01 PM
Mathasker

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)
January 5th 2006, 09:28 PM
CaptainBlack

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 $DIS$ from $A(u,v)$ define a circle with equation:

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

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

RonL
January 6th 2006, 11:30 AM
ticbol

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)