In the plane rectangular coordinate system, the coordinates of points a, B and C are (0,1), (4,2), (2,6) respectively. If P (x, y) is a point on the area (including boundary) enclosed by △ ABC, then when the maximum value of ω = XY is taken, the coordinates of point P are______ ．

In the plane rectangular coordinate system, the coordinates of points a, B and C are (0,1), (4,2), (2,6) respectively. If P (x, y) is a point on the area (including boundary) enclosed by △ ABC, then when the maximum value of ω = XY is taken, the coordinates of point P are______ ．

∵ the coordinates of points a, B and C are (0,1), (4,2), (2,6) respectively. The area (including boundary) enclosed by ∵ ABC is shown in the following figure: from the figure, when ω = XY reaches the maximum value, point P is on line BC, and the point on line BC satisfies: y = - 2x + 10, X ∈ [2,4], and ∵ ω = xy = x (- 2x + 10), so when x = 52, y = 5, ω reaches the maximum value