Has vertices of a(0, 0), b(–4, 0), and c(–2, 4). the coordinates of each vertex are multiplied by 3 to create . determine if is similar to . explain your answer.

Coordinates of vertices of new triangle:
A´(0,0), B´(-12,0), C´(-6,12).
This transformation is dilatation, with the origin as the center of dilatation and the scale factor of the dilatation : s=3.  A dilatation changes the size of a figure, while the shape of figure does not change.
Triangle A´B´C´ (image) is similar to triangle ABC (pre-image) because their corresponding angles are equal in measure and the ratio of their corresponding sides are in proportion (in attachment).