Tetris Transformations

Pre-Algebra · Axiom Academy

Every time you slide or spin a Tetris piece, you're doing real geometry — a translation or a rotation that keeps the piece the same shape. 1. Sliding a Piece Is a Translation Watch the L-piece slide right , then down . Notice that every square moves by the same amount, in the same direction — the piece arrives looking exactly as it started. That "move everything together" idea is a translation . In coordinates, a translation just adds the same numbers to every point. Slide right by a and down by b : Add a to every x, add b to every y Here is the L-piece moving right 2 , so every x grows by 2 while every y stays put: 2. Spinning a Piece Is a Rotation Press play and watch the T-piece turn a quarter turn — 90° clockwise — around its center square . The center stays fixed, like a pin, while the other squares swing around it. The piece looks turned, but it is still the same four-square T. Every rotation needs a fixed point. In Tetris the piece turns about its own center square (the red dot). Tetris rotations are 90° each press — a quarter of a full circle, here turning clockwise. The squares change places but their distances from the center never change — it stays a T. A 90° clockwise turn sends each point (x,y) to , measured from the center. Take the T-piece's right arm at (1,0) , measured from the center. A 90° clockwise turn sends it to (0,-1) — it swings from pointing right to pointing down, exactly as the animation shows. 3. Four Quarter-Turns Make a Full Circle

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