Question

Parallelogram ABCD is reflected over the y-axis, followed by a reflection over the x-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete? Parallelogram ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 1, 3. D is at negative 2, 1. (−5, −1) (5, 1) (−5, 1) (5, −1)

Answer 1

The point A (-5,1) undergo 3 translations which are:

Reflected over the y-axis,
x=-x'
A (-5,1)  ---->A' (-5,-1)

followed by a reflection over the x-axis,
y=-y'
A (-5,-1)  ----> A' (5,-1)

and then rotated 180 degrees about the origin
x=-x'
y=-y'
A (5,-1)  ----> A' (-5,1)

The point A is return to the original point which is A (-5,1)