Question

1. is the transformation given by ((x, y) \to (2x + 2, y + 1)) a translation? explain your reasoning.

Explanation:

A translation is a rigid transformation that shifts all points by a constant vector without scaling or rotating. The given transformation has a scaling factor (2x) in the x-component, which changes the size of the figure. Thus, it includes a dilation, not just a translation.

Answer:

No, the transformation is not a translation because it involves scaling (multiplying x by 2) in addition to shifting, while translations only involve constant shifts without scaling.