How would you construct a segment perpendicular to a given segment that goes through a point on the given segment? put the steps in order.
a. select a point clearly not on the given segment and not perpendicular.
b. using this point as the center, use a compass to draw a circle with the radius as the distance from the chosen point to the given point. it should intersect with the given segment at another location.
c. draw the diameter of the circle with a straightedge from the circle and segment intersection to the other side of the circle.
d. connect this final point (on the circle but not on the given segment) with the original point to construct a segment perpendicular to the given segment at that point.