As I stated before, a composition of transformations is a series of transformations done on an image. In this composition, we complete a translation, reflection, then rotation which is written out as "R-90*r y-axis*T{0,-4}". The first transformation is a translation of {0,-4} or {x+0, y-4}. Point A is (2,2) and you would change it to {2+0, 2-4} which would end up being (2,-2) which is what A' is. The next transformation is a reflection over the y-axis. To do this, you need to change (x,y) to (-x,y). Point A' is (2,-2) and it when you apply the rule, it turns into (-2,-2) which is point A'' which proves that we did the reflection correctly. The last translation is a rotation of -90 degrees. The rule for a rotation of -90 degrees around the origin is (y,-x). When we apply the rule onto point A'' which is (-2,-2) we come up with (-2,2) which is point A'''. This proves that we completed the rotation correctly.