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Translate a triangle and scale it in each coordinate direction
Consider a triangle with vertices in 2D plane given by (0, 0), (1, 0) and (0,1) (called unit triangle). Translate it by (1, 1) and then scale in each coordinate direction by 1/2. You get a triangle with vertices (1/2, 1/2), (1, 1/2) and (1/2, 1). Now if you first scale by 1/2 and then translate it by(1,1), you will get a different triangle with vertices (1,1), (3/2,1), (1,3/2) .
interactive picture-construction techniques
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