  Understanding the mechanical properties of glasses remains elusive since the
glass transition itself is not fully understood, even in well studied examples
of glass formers in two dimensions. In this context we demonstrate here: (i) a
direct evidence for a diverging length scale at the glass transition (ii) an
identification of the glass transition with the disappearance of fluid-like
regions and (iii) the appearance in the glass state of fluid-like regions when
mechanical strain is applied.
  These fluid-like regions are associated with the onset of plasticity in the
amorphous solid. The relaxation times which diverge upon the approach to the
glass transition are related quantitatively.
