What do you think of this math explanation?

It is sometimes taught in high school that if you take the point (a,b) where a > 0 and b > 0 and rotate it 90 degrees along the circle with center at (0,0), you get the point (-b,a).

I was trying to think of a visual explanation and came up with this Form the rectangle having vertices (a,b), (a,0), (0,b) and (0,0). When you rotate the point, drag the rectangle along with it. The image of the rectangle vertices along the axes is (0,0), (-b,0) and (0,a). Therefore the coordinates of the image of the point must be (-b,a).

This relates to the fact that the slope of a line perpendicular to a line with slope m has slope -1/m. The slope of the line joining (a,b) to the origin is m = b/a and the slope of the perpendicular is -a/b = -1/m.