SOLUTION: Suppose that vectors [a, b] and [c, d] are perpendicular. Show that ac + bd = 0.

The vector < a,b > when placed with tail at the origin 
(0,0) and tip at point (a,b) has slope: 



Similarly, The vector < c,d > when placed with tail at 
the origin (0,0) and tip at point (c,d) has slope: 



Since they are given to be perpendicular, their slopes
and opposite signed reciprocals.

Thus .

Multiply both sides by ad





Edwin