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

Correct answer is D

Step-by-step 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).

step-by-step explanation:

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .