Question

Parallelogram efgh has been reflected across the x axis and then rotated 180 degrees around the origin. which of the following transformations would return the parallelogram to it's original position?

a. reflection across the line y=x
b.reflection across the x-axis
c.reflection across the x-axis and then reflection across the y-axis
d.reflection across the y-axis <--- (this one??)

Answer 1

You are correct, it would be a reflection across the y-axis. I am great at visualizing but for those who are not (Not saying you) all they have to do is cut out a parallelogram and mimic the movements.

Answer 2

Correct answer is D

Explanation:

Parallelogram EFGH has been reflected across the x-axis to form the parallelogram ABCD. The reflection across the x-axis has a rule:

(x,y)→(x,-y).

Then parallelogram ABCD has been rotated 180° around the origin to form the parallelogram IJKL. This transformation has a rule:

(x,y)→(-x,-y).

Both these transformation together have a rule:

(x,y)→(x,-y)→(-x,y)

i.e.

(x,y)→(-x,y).

If you have to return the parallelogram to it's original position, then point (-x,y) should turn in point (x,y). So you have to apply the rule:

(x,y)→(-x,y)

that is reflection across the y-axis (see attached diagram for illustration).