After dilating MNPQ with a scale factor of 2 and translating it, the resulting shape M''N''P''Q'' is similar to the original shape MNPQ because the size changed due to dilation but the shape did not change.
Step-by-step explanation:
To answer the student's question regarding the congruency or similarity of the two shapes MNPQ and M''N''P''Q'', it's important to understand the effect of the dilations and translations applied to the original shape.
Firstly, dilating shape MNPQ by a scale factor of 2 about the origin means that each vertex of the shape will move away from the origin such that its distance from the origin is twice its original distance. This new shape will be denoted as M'N'P'Q'.
Secondly, translating this new shape M'N'P'Q' right by 1 unit and down by 3 units only shifts the position of the shape without altering its size or shape. This translation results in the final shape M''N''P''Q''.
Since dilation with a scale factor of 2 changed the size of the original shape and the translation only altered its position, MNPQ and M''N''P''Q'' are similar. They maintain the same shape, but their sizes are different due to the dilation.