The Dative with Verbs of Motion

Дательный падеж c глаголами движения

The dative with the preposition к is used to indicate the person who is the aim of the motion

or an object or a place to which motion is directed.

The dative answers the questions к кому? (to whom?), к чему? (to what?)

In answer to the question к кому? only the dative with the preposition к is used in the case of animate nouns:

Я иду к преподавателю. - I am going to my teacher.