Transformation Playground

Pre-Algebra · Axiom Academy

Slide, flip, turn, and resize a shape on the grid — and watch its coordinates change by a rule you can predict. There are only a handful of ways to move a shape around a coordinate grid: you can slide it, flip it, turn it, or resize it. Each one is called a transformation , and the surprise is that every one of them does something simple and predictable to the shape's coordinates — once you see it move, you can write the rule. Watch one little triangle take all four moves in turn. The faint triangle is where it started; the solid one is where it lands. Keep an eye on its size: the first three moves leave it exactly the same size, and only the last one changes it. Slide, flip, turn — same shape, same size. Resize — same shape, new size. Choose a transformation, then nudge the amount. Watch vertex A travel from its start to its new home — and watch the rule beneath it spell out exactly what happened to the coordinates. Every move is just arithmetic on (x, y) . Slide adds. Flip negates a coordinate. Turn swaps-and-negates. Resize multiplies. Same size, or just the same shape? Here's what splits the four moves into two camps. Pick a transformation and watch the size meter : a slide, flip, or turn drops the shape somewhere new but never changes how big it is — that's a rigid move, and the result is congruent . A resize keeps the same shape but a different size — that's similar . Rigid moves (slide, flip, turn) give congruent copies. Dilation gives a similar one.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.