Construction 1.3 Constructing of a perpendicular to a line through a point P on the  line $L$.
a.  Construct a circle with center at P .
b. Find the points of intersection between the circle and the line $L$.  ($P$ is the midpoint of these two points).
c.  Let us call these two points in previous step $A$ and $B$. We create two circles centered at $A$ and $B$ with radius $m( \overline{AB})$.
d. Find the points of intersection of these two circles.
e. Use these two points to to contruct the line through $P$.
f. Use the Show/Hide Object Tool to hide the circles. 
Why is this a perpendicular line to $L$?

$L$

P = (1.3323156023154912, 0.23059669933679625)
B = (5.65575452054923, 0.27340302525990245)
a = Line(P, B)