To find the coordinates of the image of triangle ΔABC after a dilation centered at the origin with a scale factor of 1.5, we can use the formula for dilation:
\[ (x', y') = (kx, ky) \]
where \((x, y)\) are the original coordinates, \(k\) is the scale factor, and \((x', y')\) are the new coordinates after dilation.
Given the scale factor \(k = 1.5\), we will apply this to each vertex of triangle ΔABC.
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For point A (–6, –3): \[ A' = (1.5 \cdot -6, 1.5 \cdot -3) = (-9, -4.5) \]
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For point B (7, –7): \[ B' = (1.5 \cdot 7, 1.5 \cdot -7) = (10.5, -10.5) \]
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For point C (0, 3): \[ C' = (1.5 \cdot 0, 1.5 \cdot 3) = (0, 4.5) \]
Thus, the coordinates of the image of triangle ΔABC after dilation are:
- \(A' (-9, -4.5)\)
- \(B' (10.5, -10.5)\)
- \(C' (0, 4.5)\)
The correct answer is: A (–9, –4.5), B (10.5, –10.5), C (0, 4.5)