Two transformations take place, the resultant change is A(x,y) ---A''(x+4, y-6), 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
if you need to fix a problem, don't repost the whole thing again. Just edit your original post. Wastes time checking all the redundant posts.
Since the question specifies that there was an initial reflection, the only way to wind up with no reflection is to have a second reflection to cancel it:
A(x,y) -> A'(-x,y) -> A"(-x+4,y-6)
or
A(x,y) -> A'(x,-y) -> (x+4,-y-6)
Thank you for answering, still I don't completely know how looking at A''(-x+4,y-6) you can determine there is a second reflection, I know first reflection over Y will be A' (-x,y), but do you get that the second is a reflection too and it is not a rotation.
To understand why the second transformation is a reflection, let's break down the given transformations step by step:
1. Reflection in the y-axis: A reflection in the y-axis would change the sign of the x-coordinate while keeping the y-coordinate unchanged. So, the original point (x, y) would become (-x, y).
2. Translation: The translation is defined as shifting a point by a constant amount in both x and y directions. In this case, we are shifting the point by 4 units in the positive x direction and 6 units in the negative y direction. Therefore, the original point (-x, y) would become (-x + 4, y - 6) after the translation.
Now, let's combine both transformations:
Starting with A(x, y) = (-x, y) after reflection in the y-axis,
Applying the translation: (-x, y) + translation (4 units in x direction and -6 units in y direction),
we get A''(x + 4, y - 6).
Therefore, the resultant transformation is a reflection followed by a translation. It is important to note that the teacher might have missed mentioning the translation part and only mentioned the reflection.