As shown in the figure, it is known that in the plane rectangular coordinate system, point a (0,2) and point B (2,0) pass through the intersection line ab of the origin at point C, Let BC = t, the coordinates of point P (2, y) (1) find the coordinates of point C (expressed by the algebraic formula containing T) (2) find the function analytic formula of Y with respect to t, and write out the value range of T. (3) when the triangle PBC is an isosceles triangle, find the coordinates of point P

As shown in the figure, it is known that in the plane rectangular coordinate system, point a (0,2) and point B (2,0) pass through the intersection line ab of the origin at point C, Let BC = t, the coordinates of point P (2, y) (1) find the coordinates of point C (expressed by the algebraic formula containing T) (2) find the function analytic formula of Y with respect to t, and write out the value range of T. (3) when the triangle PBC is an isosceles triangle, find the coordinates of point P

1) Let CD ⊥ ob △ CDB be an isosceles right triangle ⊥ CD: DB: CB = 1:1: √ (2) ⊥ CD = DB = √ (2) t / 2od = 2 - √ (2) t / 2 ⊥ point C coordinate is (2 - √ (2) t / 2, √ (2) t / 2) 2) be ch ⊥ BP ∵ quadrilateral cdbh is a square ⊥ ch = CD ⊥ {OCD =} HCP} CDO =} CHB ≌ △ CHP ≌

In the plane rectangular coordinate system with o as the circle point, the coordinates of point a are (0,4), and the moving point B starts from the origin and moves to the right on the x-axis. Take the line AB as the edge and make the square ABCD on its left. Point E is the intersection of the Y-axis (on the origin) and one side of the square ABCD, and let ob = T. (1) when t = 3, find the coordinates of point C; (2) use the formula containing T to represent the coordinates of point C; (3) during the movement of point B, find the coordinates of point C, Is there a time when point E is exactly the midpoint of one side of square ABCD? If so, ask for the coordinates of point C; if not, explain the reason

If you make a square ABCD on the left side of line AB, then the intersection e of one side of ABCD (which can be BC or CD) and y-axis should be on the negative half axis of y-axis
(1) As shown in Figure 1 (when 0