Final answer:
The question involves a geometric transformation applying first a dilation with a scale factor of 3, followed by a translation using the vector < -2, -2 >. The dilated coordinates (3x, 3y) are shifted according to the vector resulting in new coordinates (3x - 2, 3y - 2).
Step-by-step explanation:
Understanding Scale Factor and Translation
When working with geometrical transformations, it is common to perform a series of operations, such as dilations and translations. Dilation involves resizing an object by a scale factor, while translation involves moving every point of an object by a certain distance in a given direction, represented by a vector.
To answer the question, one would start by increasing the size of the figure by a scale factor of 3. This means that each dimension of the original figure is tripled. After the figure has been dilated, it is then moved (or translated) according to the vector < -2, -2 >. This means that the entire figure is shifted to the left by two units and down by two units on the coordinate plane.
If the original point coordinates are labeled as (x, y), after dilation they would become (3x, 3y) as a result of the scale factor of 3. The subsequent translation would adjust these coordinates to become (3x - 2, 3y - 2), incorporating the vector < -2, -2 >.