Why are vectors  and <-b,a> perpendicular? If i have the vectors:
X = {a, b}
Y = {-b, a}
How can I explain that these vectors will always be perpendicular? I know I can prove this very easily via the dot product, but I need to explain it in a layman's way. 

One way: Show that the triangle built on them satisfies the Pythagorean theorem, which implies that it's a right triangle
Another way: Show that the four points $(a,b)$, $(-b,a)$, $(-a,-b)$, and $(b,-a)$ form a rhombus, each of whose vertices are equidistant from the center. This implies that they form a square.
A third way: Form the right triangle with vertices $(0,0)$, $(0,b)$, and $(a,b)$. In addition, form the right triangle with vertices $(0,0)$, $(0,a)$, and $(-b,a)$. Observe that these are congruent, and fill in the angles.
