Anna claims she has discovered a method for determining the general form equation of a line that is perpendicular to a give line?

A perpendicular line has a negative inverse slope.
Slope is m in the equation y = mx +b

Ax+By+C=0
by = -ax
y = -a/b x
⊥ would be +b/a

Looking at the 2nd equation:
Bx-Ay+C=0
-ay = -bx
y = -b/-a x
y = b/a x

Yes, they are ⊥

Anna sounds like a real khunt

Ax + By +C=0 this gives
y = -A x/D - C/D.
slope
-A/D = tan theta. New line should be perpendicular to it
-A/D = tan (theta+pi/2)= sin(theta+pi/2)/cos( theta+pi/2)= cos theta/(-sin theta)= - 1/ tan theta. The new slope is D/A. We write
y = D/A x + f, This gives
Ay - Dx -fA=0. This is the new line.