Question

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. Without changing the width of the compass, place the compass at Q and draw an arc similar to the one drawn.

B. the compass at N and adjust the width to the widest point on arc PS.

C. Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn.

D. Place the compass at N and adjust the width to a length that is greater than the length of segment NS.

Answer 1

The best and most correct answer among the choices provided by the question is the third choice .

In constructing a parallel line, "Without changing the width of the compass, place the compass at S or P and draw an arc similar to the one drawn."

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 2

Answer with explanation:

In the figure Line segment L M is drawn.

Draw Ray NQ passing through Passing through N , which lies on line segment LM.

Placing the Compass nib on the point N,and then Draw an arc cutting line LM at point S and ray NQ at point P.------(1)

To draw a line parallel to line LM

Keeping the Width of Compass Same, place the compass at Q, and draw an arc similar to arc drawn in step 1 alternate to ∠QNM. Suppose it cuts ray NQ at point A,from A mark an arc on the semicircle drawn,suppose the arc cuts the semicircle at point G.Draw segment QG,passing through Q and G.

Option A. Without changing the width of the compass, place the compass at Q and draw an arc similar to the one drawn.