He looked through the code and found a mistake in your tables of rotations and reflections. Your time machine does a series of translations, rotations and reflections through four-dimensional space. Unfortunately, your programmer put in the wrong coordinate transformations in your master table.
Euclid is too excited about building his own computer to help you complete the task so you're on your own. Simply select the name of the transformation that corresponds to each of the possible coordinate changes below. There are four rotations (90, 180, 270 & 360°) and four reflections (across four different lines: the x-axis, the y-axis, the line y = x, and the line y = –x).
Good luck!
(If you're thinking about just guessing, there are 8*7*6*5*4*3*2*1 = 40,320 possible answers!!!)
| Keep x & y | New x: keep sign | New x: change sign |
|---|---|---|
| New y: keep sign |
(x,y) → (x,y) |
(x,y) → (-x,y) |
| New y: change sign |
(x,y) → (x,-y) |
(x,y) → (-x,-y) |
| Switch x & y | New x: keep sign | New x: change sign |
|---|---|---|
| New y: keep sign |
(x,y) → (y,x) |
(x,y) → (-y,x) |
| New y: change sign |
(x,y) → (y,-x) |
(x,y) → (-y,-x) |
Complete the tables to fix your time machine!
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