For this problem we need to identify the correct transformation between the two figures given.
Let's analyze one by one the options:
Reflection across the y-axis. (x,y) --> (-x,y)
That's False since we have the same coordinates for both figures and not makes sense.
Translation up 10 units. (x, y) --> (x, y=10)
That's False since if we select any y coordinate for any point and we see the corresponding pair we can see that the distance between both numbers is not 10
Rotation 180°. (xy) ->(-x,-y)
False again we need to satisfy the transformation for all the points of both figures and we can see that for A and A' that's not true.
Reflection across the x-axis. (x, y) --> (x, -y). CORRECT
That represent rhe correct answer since for each coordinate pair we can see that we satisfy the conditions given by the linear transformation (x, y) --> (x, -y)
