# Boldly Folding (part 1)

Algebra Level 3

You have a rectangular piece of paper of width $$W$$ and length $$L$$. You pick up the left side and fold it to the right side, like so:

Which function describes the new position of a point $$P = (x, y)$$ on the paper after the fold?

1. $$f(x, y, W, L) = \left\{ \begin{array}{rl} (W-x,y) &\mbox{ if x<\frac{W}{2}} \\ (x, y) &\mbox{ otherwise} \end{array} \right.$$

2. $$f(x, y, W, L) = \left\{ \begin{array}{rl} (W^{2}-x,y+L-W) &\mbox{ if x>\frac{W}{2}} \\ (x, y) &\mbox{ otherwise} \end{array} \right.$$

3. $$f(x, y, W, L) = (W - x, L-y)$$

4. $$f(x, y, W, L) = (\frac{\pi x}{W}, \frac{y}{\pi L})$$

Details and assumptions:

• The paper has infinitesimal thickness.
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