Question

a geographic transformation is described algebraically as shown below. (x,y) -> (3x, 3y) which best describes this transformation? a translation 3 units up and 3 units to the right a translation 3 units down and 3 units to the left a 180 degree rotation centered at the point (3, 3) a dilation with a scale factor of 3 centered at the origin

Explanation:

Step1: Recall transformation definitions

• Translation: Changes position. $(x,y)\to(x + h,y + k)$ (h: horizontal, k: vertical).
• Rotation: Changes orientation.
• Dilation: Changes size. $(x,y)\to(sx,sy)$ (s: scale factor).

Step2: Analyze given transformation $(x,y)\to(3x,3y)$

This matches dilation formula $(x,y)\to(sx,sy)$ with $s = 3$. Center - origin as no shift in formula.

Answer:

A dilation with a scale factor of 3 centered at the origin.