To find the coordinates of \( D' \) after translating the point \( D = (-9, -4) \) right by 28 units and up by 14 units, you need to add the respective translations to the x and y coordinates.
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Start with the original coordinates of \( D \): \[ D = (-9, -4) \]
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Translate right by 28: \[ x' = -9 + 28 = 19 \]
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Translate up by 14: \[ y' = -4 + 14 = 10 \]
Therefore, the new coordinates \( D' \) are: \[ D' = (19, 10) \]
So, the final answer is: \[ D' = (19, 10) \]