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

Question

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

GPT-4o mini · Answer

To construct a copy of line segment $ AB $ using point $ C $ as one endpoint: 1. **Draw a Circle Centered at Point C**: Use the compass to set the width to the length of line segment $ AB $. Place the compass point at point $ C $ and draw a circle. This circle will intersect the line segment at two points, one of which will be the where point $ B $ will be located when the segment is copied. 2. **Mark Intersection Points**: Let the intersection points of the circle and the extension of line segment $ AB $ or the position where the circle meets a line through $ C $ be marked as point $ D $ and point $ E $, depending on how far the circle intersects. The segment $ CD $ (or $ CE $) will be the copy of segment $ AB $. If you need to place both endpoints $ D $ and $ E $, you will then proceed with constructing additional segments, but this method primarily ensures you replicate the length from $ AB $ starting at $ C $. Thus, the next logical step is to draw a circle centered at point $ C $ with a radius equal to $ AB $.