Find the image of p(-3, 5) when rotated through 360o about the origin.
Property: Rotations by Multiples of 90 Degrees about the Origin
For a point with coordinates (𝑥,𝑦),the following is true:
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POINT #
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RULE
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1
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A rotation of 90 degrees results in a point with coordinates (−𝑦,𝑥)
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2
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A rotation of 180 degrees results in a point with coordinates (−𝑥,−𝑦)
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3
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A rotation of 270 degrees results in a point with coordinates (𝑦,−𝑥)
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4
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A rotation of 360 degrees results in a point with coordinates (𝑥,𝑦)
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5
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A rotation with a positive degree value indicates a counterclockwise rotation, and a rotation with a negative degree value indicates a clockwise rotation.
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6
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A rotation of −90∘ is equivalent to a rotation of 270∘, (360-90) and therefore results in a point with coordinates (𝑦,−𝑥)
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7
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A rotation of −180∘ is equivalent to a rotation of 180∘, (360-180) and therefore results in a point with coordinates (−𝑥,−𝑦)
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8
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A rotation of −270∘ is equivalent to a rotation of 90∘, (360-270) and therefore results in a point with coordinates (−𝑦,𝑥)
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9
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A rotation of −360∘ is equivalent to a rotation of 0∘, (360-360) and therefore results in a point with coordinates (𝑥,𝑦).
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From point 4, rotation of point through 360o about the origin is the same point, hence the image of rotating the point (-3, 5) through 360o will be the same, (-3, 5)
