(2) As shown in Figure ①, connect BE, draw the middle vertical line where BE intersects BC and F, connect EF, and △BEF is the crease triangle of rectangular ABCD.
The bisector of the crease is vertical, AB=AE=2,
Point a is perpendicular to BE, that is, the crease passes through point a.
∴ quadrilateral ABFE is a square.
∴BF=AB=2,
∴F(2,0).
(3) Rectangular ABCD has the largest crease triangle BEF with an area of 4,
The reasons are as follows: ① When F is near BC, as shown in Figure ②.
S△BEF≤ 1? 2? S rectangular ABCD, that is, when F and C overlap, the maximum area is 4.
② When f is on the edge CD, as shown in Figure ③,
F is FH∨BC, AB is at H point, and BE is at K point.
∫S△EKF = 1? 2? KF? AH≤ 1? 2? HF? AH= 1? 2? Rectangular AHFD,
S△BKF= 1? 2? KF? BH≤ 1? 2? HF? BH= 1? 2? S rectangular BCFH,
∴S△BEF≤ 1? 2? S rectangle ABCD = 4.
That is, when f is the midpoint of CD, the maximum area of △BEF is 4.
Let's find the coordinates of point e when the area is the largest.
① When F coincides with point C, as shown in Figure ④.
According to folding, CE=CB=4,
At Rt△CDE, ED=? CE2-CD2? =? 42-22? =2? 3? .
∴AE=4-2? 3? .
∴E(4-2? 3? ,2).
② When f is at the midpoint of the side DC, point E coincides with point A, as shown in Figure ⑤.
At this time, e (0 0,2).
To sum up, when the maximum crease area △BEF is 4, the coordinates of point E are E (0,2) or E(4-2? 3? ,2)