Final answer:
Two transformations are applied to a figure: a translation followed by a dilation with different scale factors. While the translation maintains similarity, the dilation does not have equal scale factors, so it changes the shape, making the resulting figures non-similar.
Step-by-step explanation:
The question asks whether a series of transformations applied to a figure would result in figures that are similar to the original. The transformations given are a translation (moving the figure without rotation or resizing) followed by a dilation (resizing the figure proportionally in both x and y directions). To determine similarity, we need to assess if the shapes have the same form and if the angles remain unchanged while the sides are proportional to the original.
The first transformation, ((x,y) → (x + 2, y - 1)), is a translation which does not change the size or shape of the figure, thus maintaining similarity. The second transformation, ((x, y) → (2x, 5y)), is a dilation which scales the figure by a factor of 2 in the x-direction and by a factor of 5 in the y-direction. Since these scale factors are not equal, this transformation changes the shape of the figure, resulting in a change of the angle measures, and therefore, the two figures are not similar.