Question

Which of the following transformations will produce the image overlapping the pre-image?

• A. Clockwise rotation of ${90}^o$ and again clockwise rotation by ${90}^o$
• B. Clockwise rotation of ${90}^o$ and then counterclockwise rotation of ${90}^o$
• C. Translation by 5 units toward the left and then upward translation by 5 units
• D. Translation by 3 units toward the left and then counterclockwise rotation of ${90}^o$

Answer 1

The correct option is B Clockwise rotation of ${90}^o$ and then counterclockwise rotation of ${90}^o$

In option A: Translation by 3 units toward the left and then counterclockwise rotation of ${90}^o$
The image will move 3 units toward the left and rotate by ${90}^o$ in the clockwise direction which will not produce an overlap with the preimage.
Thus, this sequence of transformations is incorrect.

In option B: Clockwise rotation of ${90}^o$ and again clockwise rotation of ${90}^o$
On a whole, this transformation will rotate the image by ${180}^o$ in the clockwise rotation which will not overlap with the original image, as overlapping needs ${360}^o$ rotation in either direction. Thus, this sequence of transformations is incorrect.

In option C: Translation by 5 units toward the left and then upward translation by 5 units
Translation toward the left and then up will take the figure to a different location altogether which will not overlap with the original image. Thus, this sequence of transformations is incorrect.

In option D: Clockwise rotation of ${90}^o$ and then counterclockwise rotation of ${90}^o$
Clockwise and then counterclockwise rotation by the same angle will yield an overlapping image, because the resulting figure will have the same location and orientation as the original figure.Thus, this sequence of transformation is correct.

➡Option D is correct.