Question

△GHJ is mapped to △G′H′J′ using each of the given rules. For which rules is △GHJ congruent to △G′H′J′?

a) (x, y)→(8x, 8y)

b) (x, y)→(x+8, y−8)

c) (x, y)→(−x, y)

d) (x, y)→(0.8x, 0.8y)

e) (x, y)→(−x, −y)

Answer 1

I'm not sure if this question is supposed to have a corresponding image. However, in dealing with congruence of an image to its pre-image, we simply need to determine whether the original image was resized or not.

Congruent images are images that are equal in measure. This will only result if the pre-image is a result of reflection, rotation, or translation.

(x, y)→(−x, y) ⇒ reflection

(x, y)→(−x, −y) ⇒ rotation

(x, y)→(x+8, y−8) ⇒ translation