Question

Which of the following transformations will result in an image that maps onto itself? A. Rotate 360 degrees. B. Reflect across the y-axis, and then reflect across the x-axis. C. Rotate 270 degrees counterclockwise, and the reflect it across the x-axis. D. Rotate 90 degrees counterclockwise, and then rotate 180 degrees.

Answer 1

Answer:

A. Rotate 360°

Step-by-step explanation:

We are required to find the transformation mapping an image onto itself.

According to the options, we have,

A. Rotate 360°.

Rotating 360° changes (x,y) to (x,y).

That is, this transformation will map the image onto itself.

B. Reflect across the y-axis, and then reflect across the x-axis.

Reflecting (x,y) across y-axis gives the point (-x,y).

Reflecting (-x,y) across x-axis gives the point (-x,-y).

So, this transformation maps (x,y) to (-x,-y).

C. Rotate 270° counterclockwise, and then reflect it across the x-axis.

Rotating 270° counter-clockwise changes (x,y) to (y,-x).

Reflecting (y,-x) across x-axis gives the point (y,x).

So, this transformation maps (x,y) to (y,x).

D. Rotate 90° counterclockwise, and then rotate 180°.

Rotating 90° counter-clockwise changes (x,y) to (-y,x).

Rotating (-y,x) by 180° counter-clockwise gives (y,-x).

So, this transformation maps (x,y) to (y,-x).

Hence, transformation in option A maps the image onto itself.