Based on your description of the last step showing two lines (one sloped and one flat) with arcs indicating equal distances from the point of intersection, it appears to represent the process of constructing a perpendicular bisector.
The sloped line suggests that it bisects an angle or a segment at right angles, and the arcs indicate that equal lengths are being maintained from a specific point along the slopes, which is characteristic of a perpendicular bisector construction.
Therefore, the type of construction being done is:
perpendicular bisector