Question

Kite ABCD is rotated 180 degrees clockwise about the origin and then reflected over the y-axis, followed by a reflection over the x-axis. What is the location of point A after the transformations are complete?

Kite ABCD is shown. A is at negative 7, 2. B is at negative 5, 3. C is at negative 2, 2. D is at negative 5, 1.

Answer 1

Coordinates of point A after rotation are A´( 7, -2 ). After reflection over the y -axis coordinates are: A´´(-7, -2).
Finally, after reflection over the x-axis: A´´´( - 7 , 2 ). It is the same as starting point A.

Answer 2

Answer: The location of A is (-7, 2)

Explanation:

When ABCD is rotated 180 degree clockwise about the origin,

Then, By the rotation of 180 degree about origin property,

The coordinates of the transformed kite,

`( - 7, 2)\rightarrow ( -(-7), -2)`

`(- 5, 3)\rightarrow ( -(-5), -3)`

`( -2, 2)\rightarrow ( -(-2), -2)`

`( - 5, 1)\rightarrow ( -(-5), -1)`

Thus, the coordinates of transformed figure after 180 degree of rotation are ( 7,-2), (5,-3), (2, -2) and (5,-1)

By the reflection over y-axis property,

The coordinates of the transformed kite,

`( 7, -2)\rightarrow (-7, -2)`

`(5, -3)\rightarrow ( -5, -3)`

`( 2, -2)\rightarrow ( -2, -2)`

`( 5, -1)\rightarrow ( -5, -1)`

Thus, the coordinates of transformed figure after reflected over y axis,

( -7,-2), (-5,-3), (-2, -2) and (-5,-1)

By the reflection over x-axis property,

The coordinates of the transformed kite,

`( -7, -2)\rightarrow (-7, -(-2))`

`(-5, -3)\rightarrow ( -5, -(-3))`

`( -2, -2)\rightarrow ( -2, -(-2))`

`( -5, -1)\rightarrow ( -5, -(-1))`

Thus, the coordinates of transformed figure after reflected over x axis,

( -7,2), (-5,3), (-2, 2) and (-5,1)

Thus, the location of A after the transformations are complete = (-7,2)