Question

second arc (centered at e)
first arc (centered at d)
a. the first arc should pass through c.
b. the first arc should be centered at c.
c. the second arc should be centered at c.
d. the second arc should cross the first arc.
e. the second arc should be centered at f.

Explanation:

Step1: Analyze the process of constructing a perpendicular line

When constructing a perpendicular line, the first arc is centered at a point (here \(D\)) on the original line \(AB\). The second arc should be centered at the intersection point of the first arc and the original line (i.e., \(F\)) to ensure the two arcs intersect properly for constructing the perpendicular.

Step2: Check each option

• Option A: The first arc is centered at \(D\), not required to pass through \(C\).
• Option B: The first arc is centered at \(D\), not \(C\).
• Option C: The second arc should be centered at \(F\) (the intersection of the first arc and \(AB\)), not \(C\).
• Option D: The second arc should be centered at \(F\) (not just cross the first arc in an un - centered way as described in the problem's incorrect centering).
• Option E: The second arc should be centered at \(F\) (the intersection of the first arc and the line \(AB\)) which is the correct construction step.

Answer:

E. The second arc should be centered at \(F\).