Question

which transformation does not preserve congruence?
a. (x, y)→(−x, −y)
b. (x, y)→(x - 5, y + 2)
c. (x, y)→(−x, y)
d. (x, y)→(2x, 2y)
o a
o b
o c
o d

Explanation:

Step1: Recall congruence - preserving transformations

Rigid - motions (translations, rotations, reflections) preserve congruence. A translation moves every point of a figure the same distance in the same direction. A rotation turns a figure around a fixed point. A reflection flips a figure over a line.

Step2: Analyze option a

The transformation $(x,y)\to(-x, -y)$ is a rotation of 180° about the origin. Rotations are rigid - motions and preserve congruence.

Step3: Analyze option b

The transformation $(x,y)\to(x - 5,y + 2)$ is a translation. Translations are rigid - motions and preserve congruence.

Step4: Analyze option c

The transformation $(x,y)\to(-x,y)$ is a reflection over the y - axis. Reflections are rigid - motions and preserve congruence.

Step5: Analyze option d

The transformation $(x,y)\to(2x,2y)$ is a dilation with a scale factor of 2. Dilations change the size of a figure and do not preserve congruence.

Answer:

D. $(x,y)\to(2x,2y)$