Question

If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A' lie?

[Hint: Place your coordinates in the blank with no parentheses and a space after the comma in the form: x, y]

Answer 1

Point A would end up at (-4, 1). After being relfected over the y-axis it would be at (4, 1), after being relfected then over the x-axis it would lie at (4, -1). Finally after being rotated 180 degrees it would end up at (-4, 1)

Answer 2

The point A' lie at (-4,1).

Explanation:

From the given figure it is clear that the coordinates of A are (-4,1).

If parallelogram ABCD was reflected over the y-axis, then

`(x,y)\rightarrow (-x,y)`

`A(-4,1)\rightarrow A_1(4,1)`

Then it reflected over the x-axis,

`(x,y)\rightarrow (x,-y)`

`A_1(4,1)\rightarrow A_2(4,-1)`

After that, it rotated 180° about the origin,

`(x,y)\rightarrow (-x,-y)`

`A_2(4,-1)\rightarrow A'(-4,1)`

Therefore the point A' lie at (-4,1).