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ScalingTransform

ScalingTransform[{sx, sy, ...}]
gives a TransformationFunction that represents scaling by a factor si along each coordinate axis from the origin.
ScalingTransform[{sx, sy, ...}, p]
gives scaling centered at the point p.
ScalingTransform[s, v]
gives scaling by a factor s along the direction of the vector v.
ScalingTransform[s, v, p]
gives scaling along the direction of v, centered at the point p.
Scaling along the coordinate axes:
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Scaling along the vector {1,1} by a factor s:
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Vectors in the scaling direction get scaled by a factor s:
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