Question 1015593: Complex numbers/trig:
Two isosceles right triangles (BAC and B'AC'; A is the right angle) share vertex A. Show that that the line bisecting line BB', passing through A is perpendicular to line CC'.
(B and B' and (C and C') are on the same side, to be clearer)
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Let A = 0, B = i, C = 1, B' = a+bi for real a,b, and C' = i(a+bi) = -b + ai. Here i(a+bi) represents a 45 degree rotation about point A.
The midpoint of BB' is (a+(b+1)i)/2, and the slope of the line bisecting BB' through A is (b+1)/a.
Line CC' has slope (0-a)/(1+b) = -a/(b+1).
Since the product of the two slopes is -1, the two lines are perpendicular.
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