What's "\(d!\)"?

Geometry Level 2

A point \((3,2) \) undergoes the following three transformations successfully:
(i): Reflection about the line \(y=x\).
(ii): Translation by a distance of 1 unit in the positive direction of \(x\)-axis.
(iii): Rotation by an angle of \(45^\circ\) about the origin in the anti-clockwise direction.

If the final position of the point is \((0, d\sqrt2) \), find the value of \(d!\).

Clarification: You have to find the value of \(d!\), not d, where \(!\) is a factorial notation.


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