Question

question 1 - 9
which representation of a transformation on a coordinate grid does not preserve distance?
$(x,y)\to(2x,2y)$
$(x,y)\to(x + 2,y + 2)$
$(x,y)\to(x,-y)$
$(x,y)\to(y,-x)$

Explanation:

Step1: Recall distance - preserving transformation

A transformation that preserves distance is an isometry. Translations, rotations, and reflections are isometries.

Step2: Analyze option A

The transformation $(x,y)\to(2x,2y)$ is a dilation with a scale factor of 2. Dilation changes the size of a figure, so it does not preserve distance.

Step3: Analyze option B

The transformation $(x,y)\to(x + 2,y + 2)$ is a translation. Translations preserve distance.

Step4: Analyze option C

The transformation $(x,y)\to(x,-y)$ is a reflection over the $x$ - axis. Reflections preserve distance.

Step5: Analyze option D

The transformation $(x,y)\to(y,-x)$ is a rotation of $270^{\circ}$ counter - clockwise about the origin. Rotations preserve distance.

Answer:

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