The correct answer is A.

Explanation: The first step in constructing a line perpendicular to line $AB$ and passing through an external point $M$ using a compass and straightedge is to place the compass needle on $M$, then draw two arcs that intersect the line $AB$. These intersections help in the next steps of the construction to create the perpendicular line.

Would you like a detailed explanation of the construction process?

Related Questions:

1. What is the next step after drawing the two arcs that intersect $AB$?
2. How do you confirm that the line drawn is truly perpendicular to $AB$?
3. Why is it important to keep the compass width the same while drawing the arcs?
4. Can this construction method be used to create a perpendicular bisector?
5. How would you construct a parallel line through $M$ instead of a perpendicular line?

Tip: Always ensure the compass width remains constant during the construction for accurate results.