To apply the translation rule \((x,y) \rightarrow (x-6,y)\) to point \(B(2, -3)\), we will subtract 6 from the x-coordinate while keeping the y-coordinate the same.
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Start with the original coordinates of point \(B\):
- \(x = 2\)
- \(y = -3\)
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Apply the translation:
- New x-coordinate: \(2 - 6 = -4\)
- New y-coordinate: \(-3\) (unchanged)
Thus, the coordinates of point \(B'\) after the translation are \((-4, -3)\).