Boldly Folding (part 1)

Algebra Level 3

You have a rectangular piece of paper of width WW and length LL. 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)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)=(Wx,Ly)f(x, y, W, L) = (W - x, L-y)

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

Details and assumptions:

  • The paper has infinitesimal thickness.
Dragon folded by Satoshi Kamiya.

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