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.

Question

anonymous · Answer

Which of these is likely to be his next step in constructing the parallel line?

Without changing the width of the compass, place the compass at Q and draw an arc similar to the one drawn.

Place the compass at N and adjust the width to the widest point on arc PS. 

Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn.

Place the compass at N and adjust the width to a length that is greater than the length of segment NS.