Two transformations take place, the resultant change is A(x,y) ---A''(x+4, y-^, This is a result of a reflection in the y axis followed by a _________ (translation, reflection, rotation).

I have the answer give by teacher as a "reflection, but I don't understand why or how the teacher comes out with a second reflection, please help

what the heck is y-^ ?

All I see is a translation.

To understand why the second transformation is a reflection, let's break down the given transformations.

1. Reflection in the y-axis: This transformation involves flipping the figure over the y-axis, which means that the x-coordinate of every point is changed to its opposite. So if we have a point (x, y), after this transformation, it becomes (-x, y).

2. Translation: A translation involves moving the figure horizontally (along the x-axis) or vertically (along the y-axis). In this case, the translation is given as (x+4, y-^) which means that the figure is moved 4 units to the right along the x-axis and "^" units down along the y-axis.

Now, to determine the resulting transformation, we need to analyze how the two transformations affect the coordinates of a point.

Suppose we have a point (x, y). After the first reflection, it becomes (-x, y). Then after the translation, it becomes (-x+4, y-^).

Now, let's analyze this resulting transformation:
- The x-coordinate is -x+4, where we have a negative and a positive term. This means that the resulting transformation involves reflecting the figure back to its original position with respect to the y-axis.
- The y-coordinate is y-^, where we have a negative shift. This means that the resulting transformation involves moving the figure down along the y-axis.

Based on the analysis, we can conclude that the resulting transformation after a reflection in the y-axis followed by a translation is a reflection.

It's possible that the teacher may have made an error in labeling the second transformation as a reflection. It should be a translation.