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What is the image of left parenthesis, 12, comma, 0, right parenthesis(12,0) after a dilation by a scale factor of one third
3
1
centered at the origin?
Answers
GPT-4o mini
To find the image of the point \((12, 0)\) after a dilation by a scale factor of \(\frac{1}{3}\) centered at the origin, you can use the formula for dilation:
\[
(x, y) \rightarrow (kx, ky)
\]
where \((x, y)\) is the original point, \(k\) is the scale factor, and \((kx, ky)\) is the new point after dilation.
In this case, the original point is \((12, 0)\) and the scale factor \(k\) is \(\frac{1}{3}\).
Now, we apply the dilation:
\[
\left( \frac{1}{3} \cdot 12, \frac{1}{3} \cdot 0 \right) = \left( 4, 0 \right)
\]
Thus, the image of the point \((12, 0)\) after a dilation by a scale factor of \(\frac{1}{3}\) centered at the origin is \((4, 0)\).
\[
(x, y) \rightarrow (kx, ky)
\]
where \((x, y)\) is the original point, \(k\) is the scale factor, and \((kx, ky)\) is the new point after dilation.
In this case, the original point is \((12, 0)\) and the scale factor \(k\) is \(\frac{1}{3}\).
Now, we apply the dilation:
\[
\left( \frac{1}{3} \cdot 12, \frac{1}{3} \cdot 0 \right) = \left( 4, 0 \right)
\]
Thus, the image of the point \((12, 0)\) after a dilation by a scale factor of \(\frac{1}{3}\) centered at the origin is \((4, 0)\).