To find the image of the point [tex]\((9,3)\)[/tex] after a dilation centered at the origin with a scale factor of [tex]\(\frac{1}{3}\)[/tex]:
1. Identify the original coordinates: The point we are starting with is [tex]\((9,3)\)[/tex].
2. Determine the scale factor: The scale factor given is [tex]\(\frac{1}{3}\)[/tex].
3. Apply the scale factor to each coordinate:
- Multiply the [tex]\(x\)[/tex]-coordinate by the scale factor: [tex]\(9 \times \frac{1}{3} = 3\)[/tex].
- Multiply the [tex]\(y\)[/tex]-coordinate by the scale factor: [tex]\(3 \times \frac{1}{3} = 1\)[/tex].
4. Write the new coordinates: The new coordinates after dilation are [tex]\((3, 1)\)[/tex].
So, the image of the point [tex]\((9, 3)\)[/tex] after a dilation by a scale factor of [tex]\(\frac{1}{3}\)[/tex] centered at the origin is [tex]\((3, 1)\)[/tex].
