To find the image of the point \((-8, 8)\) after a dilation centered at the origin with a scale factor of \(\frac{1}{4}\), we can use the formula for dilation:
\[ (x', y') = (kx, ky) \]
where \((x, y)\) is the original point, \(k\) is the scale factor, and \((x', y')\) is the new point after dilation.
In this case, the original point is \((-8, 8)\) and the scale factor \(k\) is \(\frac{1}{4}\).
Now we will apply the scale factor:
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For the x-coordinate: \[ x' = k \cdot x = \frac{1}{4} \cdot (-8) = -2 \]
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For the y-coordinate: \[ y' = k \cdot y = \frac{1}{4} \cdot 8 = 2 \]
Thus, the image of the point \((-8, 8)\) after the dilation is:
\[ (-2, 2) \]