Question

determine a series of transformations that would map figure q onto figure r.

Explanation:

Step1: Observe orientation change

Notice that Figure Q and Figure R have different orientations. A reflection across the y - axis can change the orientation. When we reflect a point $(x,y)$ across the y - axis, it becomes $(-x,y)$.

Step2: Observe position change

After reflection across the y - axis, we can see that Figure R is shifted down compared to the reflected Figure Q. Counting the vertical distance between corresponding points, we find that a translation 4 units down is needed.

Answer:

Reflection across the y - axis followed by a translation 4 units down.