Question

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

Answer 1

Rotation of 180 degrees around the origin

good luck hope this helped

Answer 2

Rotation of 180 degrees around the origin.

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.