In the two-dimensional Cartesian coordinate system, a new point P has two unknown coordinates Np and Ep. It is necessary to take at least two independent related observations for solving Np and Ep. Observations may be horizontal angles or distances, and each of them can deduce a position line. One of intersections of two position lines is the point P. In the paper, the corresponding formulae are derived. The influence of weights of position lines and included angle between two position lines on the precision of intersection point is illustrated by example.