As shown in Figure 2, when the coordinate of point B is (-1, 1), take the other two points E and F on the X axis, and EF = 1. When the line segment EF is translated on the X-axis, where is the minimum perimeter of the quadrilateral ABEF? Find the coordinates of point e at this time.

Analysis: In order to minimize the perimeter of quadrilateral A'B'EF, because the lengths of line segments AB and EF are fixed, only BE+AF is required to be minimum. To this end, we must first determine the positions of point E and point F: the intersection point A should be a parallel line of the X axis, and the line segment AA' intersects on this parallel line, so that AA'= 1, and point B' should be a symmetrical point about the X axis, connecting A'B' and intersecting. Then determine the position of point e and point f. Then, according to the undetermined coefficient method, the analytical formula of straight line A'B' is obtained, and then the abscissa of point E is obtained by making y=0, and then the coordinates of point E are obtained.

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