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How to find the coordinates of point C in high school mathematics
As shown in the figure, it is the XOY plane.

Obviously, ABGD is a square with CG=2√2.

CF is perpendicular to x axis, CE is perpendicular to y axis, GH is perpendicular to CE,

Therefore, CG=t-√2, CH=CF=- 1+t/(√2), OG= 1,

So C(t/(√2), 1-t/√2).

Actually, I don't quite agree with the establishment of the department. Too much trouble.

For example, the first question:

Connect AC, let AC∩BD=F, let EF∨PC, EF∩PA=E, obviously, PC∨surface EBD,

AE/EP=AF/FC=AD/BC=(√2)/t? , you don't need to ask for the coordinates of point C.