In the method of Hajj that Allah Most High taught Ibrahim (peace be upon him), He also taught him to stay at Muzdalifah. The Messenger of Allah (may Allah bless him and grant him peace) followed in the footsteps of Ibrahim (peace be upon him). He said,
“قِفُوا عَلَى مَشَاعِرِكُمْ فَإِنَّكُمْ عَلَى إِرْثٍ مِنْ إِرْثِ أَبِيكُمْ إِبْرَاهِيمَ”
‘Remain at your sacred ritual sites (namely, Arafah, Muzdalifah, and Mina), for you are heirs to the rites left by your father Ibrahim.’[1] From this, it is understood that Ibrahim (peace be upon him) stayed at each of these places: Arafah, Muzdalifah, and Mina.
[1]. Abu Dawud: 1919.