As gaze estimation research continues, the study can be classified into a 3D-based approach that estimates gaze orientation as an angle and a 2D-based approach that calculates the gaze position on a plane. That is, the 3D-based approach yields yaw and pitch, while the 2D-based approach yields the X and Y positions on the plane. Although research has been conducted for a long time, there is no way to compare gaze information calculated through each method. In order to calculate the 2D plane gaze position through yaw and pitch, the user's three-dimensional geometrical position information of face, camera, and the 2D plane should be considered in complexity. However, for the two approaches with the common purpose of gaze estimation, we believed that there would be a way to compare each other without complex three-dimensional considerations and complex calibrations. In this paper, we propose a method to accurately estimate the gaze position on a 2D plane through 2D geometric feature descriptor of face images for gaze orientation with machine learning. Experimental results on data in a laptop environment, the mean average error on X-axis was around 1.91 cm, and 0.71 cm on Y-axis, respectively.