Question

question: 2 sam and theos math teacher asked the class to use a compass and straightedge to construct a line perpendicular to line / through a point q 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. 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? a. sam drew two arcs from point p rather than a single arc. b. sam drew an arc that is entirely on the left side of point q. c. sam drew point p on the left side of the line instead of the right side. d. the teacher is incorrect; there is nothing wrong with sams original construction.

Explanation:

To construct a perpendicular line from a point above a given line using a compass and straight - edge, arcs need to intersect the line at two points on either side of the point on the line from which the arcs are drawn. Sam's arcs are entirely on the left side of point Q and do not intersect the line in a way that would allow for the construction of a perpendicular line.

Answer:

B. Sam drew an arc that is entirely on the left side of point Q.