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I have a line between with starting point of [X1,Y1] and ending point [X2,Y2] and I would like to draw a parallel line with the same length and angle(to the x axis) that pass through 3rd point [X3,Y3]. How can I do it?
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Sounds a lot like homework so I'll just get you started. It's really just 10th grade math. The slope of the first, reference line is
slope = (y2-y1)/(x2-x1)
So the second line has the same slope but you just use the point-slope formula of a line:
y - y3 = slope * (x - x3)
y = slope * (x - x3) + y3
Now, there is an infinite number of endpoints pairs for that second line that will satisfy the requirement that it is parallel and has the same length. To go any further will require another constraint/requirement, such as the angle from the original endpoint to the new endpoint to the new line is 90 degrees, or something like that. Otherwise, like I said, it could be anywhere.