Perpendicular Line through a Point

Traditional Approach

Circles at A and B must 
have the same radius.

\overline{AB} \perp \overline{PD}

P = (-0.5, 2.66)
S = (-3.3200000000000003, -0.06)
T = (6.92, 2.38)
a = Line(S, T)
U = (0, -0.16)
c = Circle(P, U)
A, B = Intersect(c, a)
C = (0.62, -1.9000000000000001)
d = Circle(A, C)
e = Circle(B, C)
D = Intersect(d, e, 1)
b = Line(P, D)