Question

Gary was constructing a midpoint on a given segment. However, Gary made an error on his construction. Look at his construction below and identify what Gary did wrong and summarize what he should have done to find the correct midpoint of the segment.

Answer 1

Given:

Gary was constructing a midpoint on a given segment. However, Gary made an error in his construction.

As shown, he used the compass to make two arcs and he connected the points of the intersection and this wrong

The correct way will be as follows:

To find the correct midpoint, we need to use the compass to make two arcs with a length less than the length of the line segment AC and intersect with AC

one arc from A and the other from C

Then, with a length more than AC, we will make another 4 arcs from the points of the intersection with AC two arcs over the line AC, and two arcs under AC

Then from the points of the intersection connect the line segment to intersect with AC at the midpoint.