Final answer:
To show that polygon W is similar to polygon V, the sequence of transformations must include a dilation, with options 'rotation and translation' not changing size. The correct answer is 'B. dilation and translation' as they alter size and position while maintaining shape.
Step-by-step explanation:
To determine which sequence of transformations can be used to show that polygon W is similar to polygon V, we need to understand the properties of similarity transformations. Similar figures have the same shape but not necessarily the same size. The transformations that preserve shape are dilations, rotations, and translations. A dilation changes the size of the figure but keeps the same shape, which is crucial for the similarity. Rotations and translations preserve both the shape and size of a figure; they only change its position.
With this in mind, we can conclude that the sequence that can be used to show that two polygons are similar must include a dilation, because that is the only transformation that can change the size. Neither rotations nor translations change the size of a figure. Reflections, which are not needed for similarity, can change the orientation but not the size or shape.
Therefore, the correct answer is 'B. dilation and translation', as they are the transformations that can change the size of a polygon and move it to a new position without altering its shape.