To find the coordinates of point C' after dilating triangle ABC by a scale factor of 2 with a center of dilation at the origin, we apply the following rule for dilation:
If a point \((x, y)\) is dilated from the origin by a scale factor \(k\), the new coordinates \((x', y')\) after dilation are given by: \[ (x', y') = (kx, ky) \]
In this case, the coordinates of point C are \(C(3, 0)\) and the scale factor \(k\) is 2. Thus, we have:
\[ C'(x', y') = (2 \cdot 3, 2 \cdot 0) = (6, 0) \]
Therefore, the coordinates of point C' are \((6, 0)\).
So, the answer is: Point C' is at \((6, 0)\).
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