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What is the image of (9,3) after a dilation by a scale factor of 1/3 centered at the origin?

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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].
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