Question

What is the first step to construct a line parallel to passing through an external point M, using only a compass and a straightedge?
A.Place the compass needle at any point on and set the compass width to M.
B.Place the compass needle at M and using sufficient compass width mark two arcs across .
C.Draw a line through M that intersects and mark the point of intersection.
D.Using a convenient compass width, mark two arcs through M centered at any point on .

Answer 1

B...you'd place the compass at m at a width greater than half the line and draw an arc 

Answer 2

The first step required in the construction is to place the compass needle at M and using sufficient compass width mark two arcs across. The appropriate option is B.

Construction is a process in which constructing instruments are used to draw a required shape or figure. Various methods can be used to construct a given shape provided that the image is exactly as required.

It is required in the question to construct a line parallel to AB passing though an external point M. First identify AB and point M, then place the compass needle at M and open it to a sufficient radius so as to mark two intersecting arcs appropriately. Then the other procedure or steps follows to complete the construction.

Therefore, the first step to construct a line parallel to AB passing though an external point M is to place the compass needle at M and using sufficient compass width mark two arcs across . Thus option B.

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