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Mathematics · Grades 7–10

Quarter-turn rotations

This rule rotates around the origin in the coordinate plane.

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The key idea

This rule rotates around the origin in the coordinate plane.

90° counterclockwise: (x,y) → (−y,x)

Worked examples

Rotate (-12, -21) 90° counterclockwise about the origin. Give the new x-coordinate.

(-12, -21) → (21, -12)

21

Rotate (-20, -22) 90° counterclockwise about the origin. Give the new x-coordinate.

(-20, -22) → (22, -20)

22

Try it yourself

  1. Rotate (5, 16) 90° counterclockwise about the origin. Give the new x-coordinate.

  2. Rotate (26, -17) 90° counterclockwise about the origin. Give the new x-coordinate.

Check your understanding

Answers and marking notes
  1. -16

    (5, 16) → (-16, 5)

  2. 17

    (26, -17) → (17, 26)

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.

Learning preview · teacher review required. Grade bands are approximate, not official curriculum alignment.