As shown in the figure, in the coordinate system, point a (0,4) and point B (3,0) rotate △ ABO counterclockwise around point o 90 ° so that point a falls on point C on the x-axis and point B falls on point E on the y-axis (1) Verification: AE = oc-ob; (2) find the length of CF

The two rotated triangles are congruent ∵ OC = OA, OE = ob, ∵ OA = OE + AE ∵ OC = ob + AE ∵ AE = oc-ob
(2) CE = AB = 5, triangle COE is similar to triangle AFE, that is, EF / OE = AE / CE, that is, EF / 3 = 1 / 5, EF = 0.6
∴CF=CE+EF=5+0.6=5.6

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