Find perpendicular line using points on that line

Question

I have a line (P1, P2), and a point on that line (midpoint). What equation can I used to find the perpendicular line of line (P1, P2), that passes through midpoint. The poin

Answer 1

Let define vector

D = P2 - P1  (dx=x2-x1, dy = y2-y1)

and middle point

mx = (x2+x1)/2
my = (y2+y1)/2

Perpendicular to D vector

PD = (-dy, dx)

Unit (normalized) perpendicular vector

U = (-dy / L, dx / L)
where
L = Sqrt (dx * dx + dy * dy)

And coordinates of point lying at distance F from the middle are

x = mx + U.x * F
y = my + U.y * F

or (for point at another side)

x = mx - U.x * F
y = my - U.y * F