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 Rotating slopes (Posted on 2006-03-21)
Given a line with slope y/x, find a simple formula for the slope of a second line that forms a 45 degree angle with this line (find slopes for both 45 degrees more and 45 degrees less.)
This can be done without trigonometry.

Find a general formula for any angle.
This requires trigonometry.

 Submitted by Jer Rating: 3.2000 (5 votes) Solution: (Hide) Consider the line through the origin and (x,y). Rotate it 90 degrees clockwise to (y,-x). The midpoint is ((x+y)/2,(y-x)/2) so the slope through the origin is (y-x,x+y) at an angle 45 degrees less than the original. Similar reasoning (or finding the perpendicular to this) give the slope of 45 degrees more as (x+y/x-y) For any angle a the formula for a decrease is ((y*cot(a)-x)/(x*cot(a)+y) and for and increase ((y*cot(a)+x)/(x*cot(a)-y)

 Subject Author Date re(2): Solution - how do you use it? Bractals 2006-03-22 17:59:09 re: Solution - how do you use it? Jer 2006-03-22 14:25:41 simple solution Tristan 2006-03-21 19:25:34 Solution Bractals 2006-03-21 16:39:26 Solution tomarken 2006-03-21 15:59:16

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