To find the new coordinates of point B after translating it 3 units to the right and 8 units down, we start with the original coordinates of point B, which are (1, 9).
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Translate right: Moving 3 units to the right means we add 3 to the x-coordinate: \[ x' = 1 + 3 = 4 \]
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Translate down: Moving 8 units down means we subtract 8 from the y-coordinate: \[ y' = 9 - 8 = 1 \]
Putting it together, the new coordinates \( B' \) after the translation are: \[ B' = (4, 1) \]
So the coordinates of point B after the translation are \( \boxed{(4, 1)} \).
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