geometry (math)

Question

Which transformation will result in an image that is congruent to its pre-image?

A.  (x, y) → (2x, −2y) 

B. (x, y) → (x, y − 2) 

C. (x, y) → (−x, 2y) 

D. (x, y) → (−2x, y − 2)

Answer 1

A transformation is congruent to its pre-image if it preserves the size and shape of the original object. This means that the transformation should not change the distances between points in the pre-image.

Option B, which translates the image 2 units down, is the only transformation that will result in an image that is congruent to its pre-image. This is because a translation does not change the shape or size of the pre-image, it simply moves it to a new position while preserving the distances between points.

Option A scales the x-axis by a factor of 2 and the y-axis by a factor of -2, which will change the size and shape of the pre-image.

Option C reflects the pre-image over the y-axis and scales the y-axis by a factor of 2, which will change the shape and size of the pre-image.

Option D scales the x-axis by a factor of -2 and translates the image 2 units down, which will change the size and shape of the pre-image.

Therefore, the correct answer is option B.