The blue shape is a dilation of the black shape. what is the scale factor of the dilation?

We are going to evaluate a vertex of both forms.
 blue shape:
 (-5.10)
 black shape:
 (-1,2)
 As one figure is the dilatation of another then:
 k (-1,2) = (- 5,10)
 From here we know:
 -k = -5
 Equivalently:
 2k = 10
 Where we conclude:
 k = 5
  
 The scale factor of the dilation is:
 k = 5