Rectangle efgh has been reflected across the x‐axis and then reflected across the y-axis. which of the following transformations would return the rectangle to its original position?
reflection across the line y=x
reflection across the x‐axis
reflection across the y‐axis
rotation of 180 degrees around the origin

Rotation of 180 degrees around the origin.

Step-by-step explanation:

Given : Rectangle EFGH has been reflected across the x‐axis and then reflected across the y-axis.

To find : Which of the following transformations would return the rectangle to its original position.

Solution :  Rectangle EFGH has been reflected across the x‐axis

suppose coordinate of E(x,y) then after reflected over x axis E would be

( x, -y)

Now, reflect it over y axis then it would become (-x ,-y)

By the reflection 180 degree rule , (x, y) →→→(-x,-y)

Then E (-x ,-y) →→→(x , y)

Hence, it return to its original position .

Therefore, Rotation of 180 degrees around the origin.