Question 1139999

let: 
{{{L[1]}}}:{{{ y=3}}} 
{{{L[2]}}}: {{{x=3}}} 

prove that:

{{{slope(L[1]) * slope(L[2]) = - 1 }}}



origin with these two points form right triangle which has legs {{{a}}},{{{ b}}} parallel to {{{axes}}}, with say {{{a}}} horizontal and  {{{b}}} vertical 

basic idea: if a right triangle has legs {{{a}}}, {{{b}}} parallel to axes, with say {{{b}}} vertical, and you {{{rotate}}} that right triangle by {{{90}}} degrees counterclockwise, the new triangle will have vertical side {{{a}}} and horizontal side {{{-b}}}.

Slope of first triangle's hypotenuse is {{{b/a}}}.
Slope of new triangle's hypotenuse is {{{a/(-b) = -a/b}}}.

Those hypotenuses are {{{perpendicular}}}, because of the {{{90}}} degree rotation, and the {{{product}}} of their slopes is:


{{{(b/a) (-a/b) = -1}}} .....in your case {{{a=3}}}, {{{b=3}}}

{{{(3/3) (-3/3) = -1}}}

{{{(1) (-1) = -1}}}

{{{-1 = -1}}}->proven