To rotate a point \( (x, y) \) counterclockwise around the origin by \( \theta \) degrees, you can use the rotation formulas:
\[ x' = x \cos(\theta) - y \sin(\theta) \] \[ y' = x \sin(\theta) + y \cos(\theta) \]
For a 270-degree counterclockwise rotation, we note that:
\[ \cos(270^\circ) = 0 \] \[ \sin(270^\circ) = -1 \]
Now, substituting in the values for the point \( (5, 8) \):
\[ x' = 5 \cdot 0 - 8 \cdot (-1) = 0 + 8 = 8 \] \[ y' = 5 \cdot (-1) + 8 \cdot 0 = -5 + 0 = -5 \]
Thus, the new coordinates after rotating the point \( (5, 8) \) 270 degrees counterclockwise about the origin are:
\[ (8, -5) \]
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