Frankie constructed line segment `AB`using a compass and a straightedge. He then placed point C so that it was not on the segment he just constructed, as shown in the image. What is the next step Frankie must take to construct a copy of line segment AB using point C as one of the endpoints?

Answer 1

To construct a copy of line segment \( AB \) using point \( C \) as one of the endpoints, Frankie should follow these steps:

1. Measure the length of segment \( AB \): Using a compass, Frankie should place the compass point on point \( A \) and adjust it to reach point \( B \). This will set the compass width to the length of segment \( AB \).

2. Copy the length to point \( C \): With the compass still set to the length of segment \( AB \), Frankie should place the point of the compass on point \( C \) and draw an arc in the direction where he wants the other endpoint to be.

3. Label the intersection point as \( D \): The arc will intersect the line where Frankie wants to position the other endpoint of the segment. He should label the intersection point as \( D \).

4. Construct segment \( CD \): Now, Frankie simply connects point \( C \) to point \( D \) using a straightedge. The segment \( CD \) will be a copy of segment \( AB \).

By following these steps, Frankie successfully constructs segment \( CD \) that is congruent to segment \( AB \), with \( C \) as one endpoint.