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 September 16th, 2012, 02:15 PM #1 Newbie   Joined: Sep 2012 Posts: 3 Thanks: 0 Drawing a line from point a,b .. coords point b unkown Hi, Question 1: If a draw a line from (1,1) to (2,1) what angle does that line have in radians(relative to pi)? I think 0*pi Same for lets say (1,1) to (1,2) I think pi/2 or even (1,1) to (2,2) (Please use this correct answer in question 2 because I might have it wrong) I think pi/4 Question 2: I need to draw a line with given info: coords point A, an angle (radian relative to pi) and length of line. I think the solution lies using algebra on the Pythagorean theorem. Example: What are coords of point B? coords point A = (1,1) angle = pi/4 (45 degrees) {Note that this may not be what I mean which is why I asked the first question) length = sqrt(2) ~ 1,41 The answer should be (2,2) but the point is that I need to understand the algebra behind it so I can use it for more complex variables/parameters.
 September 16th, 2012, 02:29 PM #2 Member   Joined: May 2012 Posts: 78 Thanks: 0 Re: Drawing a line from point a,b .. coords point b unkown First of all, your first question is not entirely clear - angle between the line and what exactly? Second, The angle that is given is the angle between the line and the positive side of the x-axis. If there is an angle $\alpha$ between the line y=mx+n and the positive side of the x-axis, then $tan(\alpha)=m$. In your case the slope will be 1. Now you can write the equation of the line AB and set B coords accordingly to this equation. Use the length that is given and the formula of distance (which lies on the Pythagorean theorem) between points and get the coords of point B. If you have any problem, just ask.
 September 16th, 2012, 03:41 PM #3 Newbie   Joined: Sep 2012 Posts: 3 Thanks: 0 Re: Drawing a line from point a,b .. coords point b unkown First thanks a lot for the answer! One: I was hoping it was standard to reason from the x-axis when talking about angles of lines. Two: So I now know how (thx, I learned this before but forgot) to derive the slope from the angle. It gives me a feeling of which way the line should go. But I still need to know exactly where my line segment stops. It feels trivial since I know the distance, the slope and the start of the segment now but I have no idea how to use the slope in combination with the distance formula to get coords of point b. I have 2 unknowns in the distance formula and I don't seem to get how the slope can solve that problem.
 September 16th, 2012, 03:47 PM #4 Newbie   Joined: Sep 2012 Posts: 3 Thanks: 0 Re: Drawing a line from point a,b .. coords point b unkown Another problem I am thinking of is that I want also want to define line segments that are entirely vertical (Line(1,1),Line(1,2)) and the slope seems to be meaningless at that point.
 September 16th, 2012, 06:44 PM #5 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Drawing a line from point a,b .. coords point b unkown If you want to find the angle of inclination of a line segment, you may use the relation: $\frac{\Delta y}{\Delta x}=\tan\theta$ If your line segment is actually a vector, that is, it has direction, then use of appropriate trig. identities involving the tangent function will place the angle in the correct quadrant.
 September 17th, 2012, 12:28 AM #6 Member   Joined: May 2012 Posts: 78 Thanks: 0 Re: Drawing a line from point a,b .. coords point b unkown Hey, Vibonacci. Here is a full solution: From the given angle we derive that the slope is $m=tan(45)=1$. We have slope and a point [(1,1)], thus we can write the equation of the line AB - $AB \ : \ y-1=1(x-1) \right y=x$. Now we can write the coords of point B in the form (b,b). The distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$. In your case $d_{AB}=sqrt{(b-1)^2+(b-1)^2}=sqrt{2(b-1)^2}=sqrt{2}$. Square both sides - $2(b-1)^2=2 \right (b-1)^2=1$. The equation $a^2=b^2$ has two solutions - $a=\pm{b}$. In this case we get b=2 or b=0, so the point B is (0,0) or (2,2). Both answers are fit. Is it clearer now?

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