Question

b. given the hint, what steps are taken next to complete this construction?
a. find p so that m is the mid - point of pq. then pp is the required line
b. find the mid - point m of mq. then pm is the required line
c. measure the length of pq, and then draw a line segment extending mq by this amount. the endpoint of this segment is p. then pq is the required line
d. connect p with a second point r on l with mid - point n. then mn is the required line

Explanation:

To complete the construction, finding a point \(P'\) such that \(M\) is the mid - point of \(P'Q\) gives the required line \(\overrightarrow{PP'}\) as it follows the geometric principles of mid - points and vector construction. Other options do not follow the correct geometric procedure for the construction described.

Answer:

A. Find \(P'\) so that \(M\) is the midpoint of \(\overline{P'Q}\). Then \(\overrightarrow{PP'}\) is the required line.