A line segment detection apparatus includes a head that supports a sensor configured to detect light reflected by a surface of a cutting target medium, a driving unit configured to move the head in two-dimensional directions relatively to the medium, and a processing unit configured to drive the driving unit and perform arithmetic processing on an output of the sensor. The processing unit includes a region detection unit configured to detect a region different in reflectance from surroundings based on a change of a signal output from the sensor when the sensor was moved in a first direction, and a determination unit configured to determine whether the region is a line segment, based on the change of the signal output from the sensor when the sensor passed a point in the region and was moved in a second direction perpendicular to the first direction.