生成一个数学题目讲解视频，数学题目在图片内，目标受众是中国大陆高中学生，你作为一个拥有多年应试教学经验的老师，要求你至少给出1考察知识点梳理与解题思路2解题具体步骤3方法归纳与总结4相似题型分析，还可根据你的经验优化讲解流程，补充其他部分---**Extraction Content:**
**Question 3:**
As shown in the figure, in the plane rectangular coordinate system, quadrilateral OABC is a rectangle, point A(2√3, 0), point C(0, 2). Point D is a moving point on side BC. Fold ∠COD along OD to get ∠EOD. Fold point B along the line connecting point O and point F, a point on side BA, such that it falls on point G on ray DE.
(1) Fill in the blank: ∠ODF = ______ °;
(2) Assume point D(x, 2), point F(2√3, y). Find the relationship between y and x, and find the distance traveled by point F when x increases from 0 to 2√3;
(3) Under the conditions of (2), when point G falls on the x-axis:
① Prove: CD=AG;
② Find the value of x at this time.
**Diagrams:**
**图 (1):**
* Type: Geometric figure in a plane rectangular coordinate system.
* Coordinate Axes: X-axis and Y-axis are shown, intersecting at the origin O.
* Points: Labeled points are O, C, D, B, E, G, F, A.
* Shapes/Lines:
* Rectangle OABC is indicated by vertices O, A, B, C and dashed lines for sides AB and BC.
* Point O is at the origin (0,0).
* Point A is on the positive x-axis.
* Point C is on the positive y-axis.
* Point D is on the line segment BC.
* Line segment OD is shown.
* Ray DE is shown.
* Line segment OE is shown. By the folding condition, ray OE is the reflection of ray OC across OD, so ∠COD = ∠EOD. E appears to be on the line OC or its extension, or a point determined by the folding. Based on the diagram, E is shown distinct from O and C.
* Line segment OB is shown.
* Line segment OF is shown, with F on line segment BA.
* Line segment FG is shown.
* Line segment OG is shown. By the folding condition, G is the reflection of B across OF, so G lies on ray DE and OB = OG, ∠BOF = ∠GOF.
* Labels: O, A, B, C, D, E, F, G, x, y, 图 (1).
**图 (2):**
* Type: Geometric figure in a plane rectangular coordinate system, illustrating a specific case.
* Coordinate Axes: X-axis and Y-axis are shown, intersecting at the origin O.
* Points: Labeled points are O, C, D, B, G, F, A, E.
* Shapes/Lines: Similar to Diagram (1), showing rectangle OABC (dashed AB, BC) and various line segments.
* The key difference is that point G is specifically shown lying on the x-axis.
* Labels: O, C, D, B, G, F, A, E, x, y, 图 (2).
**Given Coordinates:**
* A(2√3, 0)
* C(0, 2)
* Rectangle OABC implies O(0,0) and B(2√3, 2).
* D(x, 2) with D on BC (so 0 ≤ x ≤ 2√3).
* F(2√3, y) with F on BA (so 0 ≤ y ≤ 2).