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What are the coordinate points of

𝐴
′
A
′

(
9
,

7
)
(9, 7) if
𝐴
A undergoes a rotation of:

90
°
90° clockwise

180
°
180° clockwise


270
°
270° clockwise

1 answer

To find the new coordinates after rotation, we can use the following transformations:

  1. 90° Clockwise Rotation: The formula for a 90° clockwise rotation around the origin (0,0) is: \[ (x, y) \rightarrow (y, -x) \] For point \( A' (9, 7) \): \[ A'' (7, -9) \]

  2. 180° Clockwise Rotation: The formula for a 180° rotation is: \[ (x, y) \rightarrow (-x, -y) \] For point \( A' (9, 7) \): \[ A'' (-9, -7) \]

  3. 270° Clockwise Rotation: The formula for a 270° clockwise rotation is: \[ (x, y) \rightarrow (-y, x) \] For point \( A' (9, 7) \): \[ A'' (-7, 9) \]

Summary of Rotated Coordinates:

  • 90° Clockwise: \( (7, -9) \)
  • 180° Clockwise: \( (-9, -7) \)
  • 270° Clockwise: \( (-7, 9) \)