Slide, turn, flip
Three ways to move a shape, and not one of them changes it. The faint shape is where it started; follow the marked corner to see what happened to its coordinates.
The marked corner moved (4, 2) → (7, −2) The shape itself changed by Nothing
- The move
- 3 right, 4 down
The move
Drag the shape to slide it, or use the arrow keys.
Turn about (0, 0)
Flip over
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Where it usually goes wrong
Moving a shape is thought to change it. It does not: after a slide, a turn or a flip, every side is the same length and every angle the same size — only the address changed. The related error is at the coordinates, where a flip over the x-axis is confidently reported as changing the x.
Try this
- Slide the shape and follow the marked corner. Both coordinates change, and the shape itself has changed by nothing.
- Flip over the x-axis and read the corner. It is the y that changed sign, because the x-axis is what you folded over.
- Turn 90°, then 90° again, then twice more. Four quarter turns and the shape is back where it started.
Where this goes next
Two shapes are congruent when one of these moves takes you from one to the other, which is what a proof means when it says two triangles are the same.