Question

which representation of a transformation on a coordinate grid does not preserve distance? (x,y)→(2x,2y). (x,y)→(x + 2,y + 2) (x,y)→(x, - y) (x,y)→(y, - x)

Explanation:

Step1: Recall transformation types

Rigid - motions (translations, rotations, reflections) preserve distance. Dilations do not.

Step2: Analyze each option

• $(x,y)\to(2x,2y)$ is a dilation (scaling by a factor of 2). Distance is not preserved.
• $(x,y)\to(x + 2,y + 2)$ is a translation. Distance is preserved.
• $(x,y)\to(x,-y)$ is a reflection over the x - axis. Distance is preserved.
• $(x,y)\to(y,-x)$ is a rotation of 90 degrees counter - clockwise about the origin. Distance is preserved.

Answer:

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