Question

Reflect the point A(5,1) over the y-axis and then translate it by the rule (x,y) -> (x-2,y+4). What is the location of A"?

Answer 1

After reflecting point A(5,1) over the y-axis and applying the translation rule (x,y) -> (x-2,y+4), the final coordinates for point A" are (-7, 5).

Step-by-step explanation:

To reflect the point A(5,1) over the y-axis and then apply the translation rule (x, y) -> (x-2, y+4), we perform two steps:

1. Reflection over the y-axis: This changes the x-coordinate of point A while keeping the y-coordinate the same. The reflected point, A', becomes A'(-5, 1).
2. Translation: The translation rule requires subtracting 2 from the x-coordinate and adding 4 to the y-coordinate of A'. Applying this to A', the new coordinates become (-5-2, 1+4), which simplifies to A"(-7, 5).

Therefore, after reflecting point A over the y-axis and applying the translation, the location of point A" is (-7, 5).