Question

Identify the function that models each series of transformations performed on a polygon.

A 270° clockwise rotation about the origin followed by a reflection across the x-axis.
A 90° clockwise rotation about the origin followed by a reflection across the x-axis. A reflection across the x-axis followed by a 180° rotation about the origin.

Options are:
f(x, y) = (y, x)
g(x, y) = (-y, -x)
h(x, y) = (y, -x)
j(x, y) = (-x, y)
k(x, y) = (x, -y)

Answer 1

A ------------ g(x,y) = (-y,-x)

B -------------- f(x,y) = (y,x)

C -------------- j(x,y) = (-x,y)

Explanation:

We are required to match the transformations with the corresponding function.

According to the options, we have,

A. 270° clockwise rotation about the origin followed by a reflection across the x-axis.

We know that, 270° rotation clockwise about origin will change the co-ordinates (x,y) to (-y,x).

Then, the reflection about x-axis will change (-y,x) to (-y,-x)

Thus, the corresponding function will be g(x,y) = (-y,-x).

B. 90° clockwise rotation about the origin followed by a reflection across the x-axis.

We know that, 90° rotation clockwise about origin will change the co-ordinates (x,y) to (y,-x).

Then, the reflection about x-axis will change (y,-x) to (y,x)

Thus, the corresponding function will be f(x,y) = (y,x).

C. Reflection across the x-axis followed by a 180° rotation about the origin.

We know that reflection across x-axis will change (x,y) to (x,-y).

We know that, 180° rotation clockwise about origin will change the co-ordinates (x,-y) to (-x,y).

Thus, the corresponding function will be j(x,y) = (-x,y).

So, we have the matches,

A ------------ g(x,y) = (-y,-x)

B -------------- f(x,y) = (y,x)

C -------------- j(x,y) = (-x,y)