To rotate the point (1, 2) 270 degrees clockwise around the origin, we can use the rotation formula. When rotating a point (x, y) by an angle θ, the new coordinates (x', y') can be calculated using the following formulas:
\[ x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \] \[ y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \]
For a 270-degree clockwise rotation, θ = -270 degrees (or equivalently, 90 degrees counterclockwise). We know that:
- \(\cos(90^\circ) = 0\)
- \(\sin(90^\circ) = 1\)
Plugging these values into the formulas, we have:
\[ x' = 1 \cdot 0 - 2 \cdot 1 = 0 - 2 = -2 \] \[ y' = 1 \cdot 1 + 2 \cdot 0 = 1 + 0 = 1 \]
Thus, after rotating the point (1, 2) by 270 degrees clockwise around the origin, the new coordinates are (-2, 1).
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