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