# 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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