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Identify the domain of an image that has been rotated 270 degrees counter-clockwise

about the origin, given the range is (3,-4), (1, -1), (6, -7).
O (4, -3), (1, -1), (7,-6)
O (-4, 3). (-1, 1), (-7, 6)
O (-3,-4).(-1, -1), (-6, -7)
0 (4,3), (1, 1), (7,6)

User Osmund
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1 Answer

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Final answer:

To find the domain of an image rotated 270 degrees counter-clockwise with a given range, swap and negate the y-coordinates to simulate a 90-degree clockwise rotation. The domain of the rotated image is (4,3), (1, 1), (7,6).

Step-by-step explanation:

To identify the domain of an image that has been rotated 270 degrees counter-clockwise about the origin with the given range, we must map each point of the range onto the corresponding domain through the rotation. A rotation of 270 degrees counter-clockwise is equivalent to a rotation of 90 degrees clockwise.

To perform a 90-degree clockwise rotation, you can swap the x and y coordinates of each point and then change the sign of the new y-coordinate. Given the range (3,-4), (1, -1), (6, -7), after the rotation the new coordinates will correspond to:

  • (3,-4) becomes (4,3)
  • (1,-1) becomes (1,1)
  • (6,-7) becomes (7,6)

Therefore, the domain of the rotated image is (4,3), (1, 1), (7,6).

User Tomas Langkaas
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