Question

Create a transformation that is not a similarity transformation. Use coordinate notation .

Answer 1

Answer:

  (x, y) ⇒ (2x, y)

Step-by-step explanation:

Any rigid transformation or dilation will be a similarity transformation. A transformation that doesn't preserve similarity will be none of those, so may be non-linear or different in one direction than another.

Several possibilities come to mind:

  (x, y) ⇒ (2x, y) . . . . . . stretches x, but not y

  (x, y) ⇒ (x+y, y) . . . . . a "shear" transformation

  (x, y) ⇒ (x, y^(3/2)) . . . . . a non-linear transformation

These only transform one coordinate. Of course, different transforms or combinations can be used on the different coordinates.

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The attachment shows the effect of each of these. The red figure is the original icosagon (20-gon). The blue figure shows the horizontal stretch of the first transformation. The green figure shows the diagonal stretch of the shear transformation. The purple figure shows the effect of a non-linear transformation.