Finding the coordinates of a line, having another line and an angle between them

[georgepedrosa]

If I have a line, how do I find a second line that has the same extent as the first one, and crosses the first one in a given origin point and angle?
For example, in this image I need to find x2 and y2, which are the only variables I don't have (I have x0, y0, x1, y1, d and θ):

 

[tkhunny]

Several ways to go about it.
-- Law of Cosines will find the line segment between. You may be able to solve the two circles simultaneously.
-- Note the slopes of the lines and consider the sum and difference of tangent formulas. You may see it.
-- A quick vector analysis would slice through it nicely.

Just three that come immediately to mind. Let's see what you try and how it comes out.

 

[georgepedrosa]

It's just for a software that uses vector graphics, I'm trying to create a geometric shape in the form of a protractor by doing a continuous touch gesture on a tablet. So I have all the coordinates of the line that is created by the touch gesture, and I need to create another line that is in a pre-determined angle from the first line, just like the image I provided, but I haven't been able to figure out the math to get x2 and y2.

 

[tkhunny]

It's just for a software that uses vector graphics, I'm trying to create a geometric shape in the form of a protractor by doing a continuous touch gesture on a tablet. So I have all the coordinates of the line that is created by the touch gesture, and I need to create another line that is in a pre-determined angle from the first line, just like the image I provided, but I haven't been able to figure out the math to get x2 and y2.

Okay, that sounds like the problem as you stated it the first time. Which of the three methods have you attempted?