To find the degree of rotation, we can use the coordinates of the points and apply some geometric principles.
The original point B is at (-8, 6), and the rotated point B' is at (-6, -8).
By calculating the angle of rotation, we can use the tangent of the angle formed by the vectors originating from the origin (0, 0) to each of the points.
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Find the angle for point B: \[ \tan(\theta_B) = \frac{y}{x} = \frac{6}{-8} = -\frac{3}{4} \]
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Find the angle for point B': \[ \tan(\theta_{B'}) = \frac{-8}{-6} = \frac{4}{3} \]
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Now we can use the inverse tangent to find the angles:
- For B: \[ \theta_B = \tan^{-1}\left(-\frac{3}{4}\right) \approx -36.87^\circ \]
(Location in Quadrant II, hence we add 180°): \[ \theta_B = 180^\circ - 36.87^\circ \approx 143.13^\circ \]
Resulting in approximately 143.13° as the angle corresponding to the original point.
- For B': \[ \theta_{B'} = \tan^{-1}\left(\frac{4}{3}\right) \approx 53.13° \]
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The rotation from B to B' is: \[ \text{Rotation} = \theta_{B'} - \theta_B = 53.13^\circ - 143.13^\circ \approx -90^\circ \]
Since we are looking for a positive degree of rotation, the final answer is: \[ \text{Rotation} = 270^\circ \]
Thus, B was rotated 270 degrees.
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