Vietnam today is having solid innovations in the fields of science, technology, economics, and education. In particular, the Mathematical General Education program launched in 2018 has emphasized the exploitation of information technology in teaching. GeoGebra software is taught right from the 6th grade. GeoGebra software has many advantages in problems related to motion such as locus, modeling, and especially in finding the shortest path. We have found that the discovery teaching method proves to have outstanding advantages in teaching this shortest path problem. Our research focus on understanding the perspectives of discovery teaching, the discovery teaching process, the pros and cons of the discovery teaching method, illustrating the application of GeoGebra software in the discovery teaching of finding the shortest distance. Using essential research methods such as theoretical research, investigation, survey, and descriptive statistics with the help of SPSS version 20 software for 49 students grade 12th, we found that students felt very interested in the new teaching method. Students showed excitement and enthusiasm in lessons to find the shortest distance with the help of GeoGebra software. The assessment results show that students make more progress when applying GeoGebra to teaching than traditional teaching methods.