The black shape is a dilation of the purple shape
Dilation is a transformation in which an object is made larger or smaller without changing its shape. In this case, the black shape is a dilation of the purple shape, meaning it is an enlarged or reduced version of the original purple shape.
The black shape would have similar proportions and angles to the purple shape, but its size would be different. The scale factor, which determines the amount of enlargement or reduction, can be greater than 1 for enlargement or less than 1 for reduction.
The process of dilation involves multiplying the coordinates of each point in the purple shape by the scale factor to obtain the corresponding points in the black shape. This results in the entire shape being proportionally larger or smaller while maintaining its original shape.
Overall, the black shape is essentially a scaled version of the purple shape, preserving its geometric properties but with a different size.