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 one of the endpoints?
use a compass, measure the distance between points A and B.
use a compass, measure the distance between points Band C.
use a compass, measure the distance between points A and C.

Answer 1

To construct a copy of line segment AB using point C as one of the endpoints, Frankie should use a compass to measure the distance between points A and B. Here’s the step-by-step reasoning:

1. **Measure the Length of AB:** Using a compass, Frankie should place the pointer of the compass at point A and stretch the compass to point B. This will give him the exact length of segment AB.

2. **Place the Compass on Point C:** After measuring the distance AB, Frankie should then place the pointer of the compass at point C and draw an arc that is the same length as segment AB.

3. **Mark the End of the Arc:** The point where the arc intersects will represent point D, which is the other endpoint of the new segment CD.

By this process, Frankie can successfully create a new line segment CD that is congruent to AB, with point C as one endpoint.