Question

a student is copying a segment \\( \overline{ab} \\) using only a compass and a straightedge. the student completed the following steps:

1. draw a point c
2. place the compass on point a and adjust it to the length of segment \\( \overline{ab} \\).

what is the next step the student should complete to finish copying the segment?
\\( \circ \\) place the compass on point a and draw an arc.
\\( \circ \\) use the straightedge to draw a line through points a and b.
\\( \circ \\) draw a circle centered at point a that passes through point b.
\\( \circ \\) without changing the compass length, place the compass on point c and draw a small arc.

Explanation:

Step1: Recall segment copying steps

To copy segment \(\overline{AB}\) to a new point \(C\), after setting compass to length \(AB\) (by placing on \(A\) and adjusting to \(B\)), the next step is to use that compass length (without changing) and place the compass on \(C\) to draw an arc (this arc will help mark the endpoint of the copied segment).

Let's analyze each option:

• "Place the compass on point \(A\) and draw an arc": This doesn't help copy to point \(C\), so incorrect.
• "Use the straightedge to draw a line through points \(A\) and \(B\)": This is part of the original segment, not copying to \(C\), incorrect.
• "Draw a circle centered at point \(A\) that passes through point \(B\)": We already set the compass length, but we need to work from point \(C\), not draw a circle at \(A\) for copying, incorrect.
• "Without changing the compass length, place the compass on point \(C\) and draw a small arc": This is the correct next step as it uses the compass length (equal to \(AB\)) from point \(C\) to start marking the copied segment.

Answer:

Without changing the compass length, place the compass on point \( C \) and draw a small arc.