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)

Explanation:

Step1: Identify transformation types

a. $(x,y)\to(-x, -y)$ is a rotation of 180 - degrees about the origin. Rotations preserve congruence.

Step2: Analyze second transformation

b. $(x,y)\to(x - 5,y + 2)$ is a translation. Translations preserve congruence.

Step3: Analyze third transformation

c. $(x,y)\to(-x,y)$ is a reflection over the y - axis. Reflections preserve congruence.

Step4: Analyze fourth transformation

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

Answer:

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