An architect plans to draw a rectangular patio with segment LM representing one side of the rectangle. He wants to construct a line passing through Q and parallel to side LM. He uses a straightedge and compass to complete some steps of the construction as shown.
Which of these is likely to be his next step in constructing the parallel line?
A. Draw a line from Q to the midpoint of LM.
B. Draw a line from Q to the endpoint of LM.
C. Draw a line from Q to the intersection of the two arcs.
D. Draw a line from the midpoint of LM to the intersection of the two arcs.
Answer: B. Draw a line from Q to the endpoint of LM.
The architect's likely next step in constructing the parallel line would be to use a compass to measure an equal distance from point Q along segment LM, and then mark a new point on the opposite side of segment LM.
To construct a line passing through point Q and parallel to side LM, the architect has already used a straightedge and compass for some steps of the construction. However, the steps are not provided in the question, so it's difficult to determine the architect's exact progress or which construction technique was used.
That being said, a common method to construct a parallel line is to use a compass to mark equal distances on both sides of point Q along segment LM. Then, use a straightedge to connect the two marked points, which will create a parallel line to segment LM passing through point Q.
If this is the approach the architect is following, his next step would likely involve measuring equal distances on both sides of point Q along segment LM using a compass, and then using a straightedge to connect the two marked points to construct the parallel line.