Question 1182584
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Draw the first line, slope m1, ending at point (a,b), r units out from the origin and making an angle {{{alpha}}} with respect to the x-axis:

   m1 = b/a = {{{ (r*sin(alpha)) / (r*cos(alpha)) }}}

Now draw a 2nd line with slope m2, length r units, rotated 90 degrees with respect to the first line.  The endpoint at r units out is (c,d):

Make use of this identity:  {{{ cos(alpha+beta) = cos(alpha)cos(beta)-sin(alpha)sin(beta)}}}

   c = {{{ r*cos(alpha + 90) = -r*sin(alpha) }}}

Make use of this identity: {{{ sin(alpha+beta) = sin(alpha)cos(beta)+cos(alpha)sin(beta) }}}
   d = {{{ r*sin(alpha + 90) = r*cos(alpha) }}} 


Noting m2 = d/c, you can now write:

   m1*m2 = (b/a)(d/c) = {{{ ((r*sin(alpha)) / (r*cos(alpha))) * ((r*cos(alpha))/(-r*sin(alpha))) }}} = -1,  with the constraint neither slope is zero.