# 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.