Sam and Theo's math teacher asked the class to use a compass and straightedge to construct a line perpendicular to line through a point located above the line.
Sam and Theo each began their constructions by drawing arcs from a point P on the
line. Their work is shown below.
Sam's Work
Theo's Work
After inspecting their figures, the teacher advised Theo to continue with the
construction. However, the teacher told Sam that he would have to start over because
his construction had a serious flaw and could not be completed
What did Sam do that makes it impossible for him to correctly complete the
construction?
Sam drew two arcs from point P rather than a single arc.
Sam drew an arc that is entirely on the left side of point Q.
The teacher is incorrect; there is nothing wrong with Sam's original
construction
Sam drew point P on the left side of the line instead of the right side.