Question

which transformation will preserve the size and orientation of its proimage?
a. $(x,y)\to(2x,2y)$
b. $(x,y)\to(-x,y)$
c. $(x,y)\to(x + 3,y + 1)$
d. $(x,y)\to(y,x)$

Explanation:

Step1: Analyze Option A

The transformation \((x,y)\to(2x,2y)\) is a dilation. Dilation changes the size of the figure.

Step2: Analyze Option B

The transformation \((x,y)\to(-x,y)\) is a reflection over the \(y -\)axis. Reflection changes the orientation.

Step3: Analyze Option C

The transformation \((x,y)\to(x + 3,y+1)\) is a translation. Translation preserves the size and orientation of the pre - image.

Step4: Analyze Option D

The transformation \((x,y)\to(y,x)\) is a reflection over the line \(y=x\). Reflection changes the orientation.

Answer:

C. \((x,y)\to(x + 3,y + 1)\)