Rotations on the Coordinate Plane Flashcards

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Questions and Answers

What is (x,y) rotated to when it undergoes a 90° CCW angle rotation around the origin?

  • (-x,-y)
  • (x,y)
  • (y,-x)
  • (-y,x) (correct)

What is (x,y) rotated to when it undergoes a 90° CW angle rotation around the origin?

  • (y,-x) (correct)
  • (-x,-y)
  • (x,y)
  • (-y,x)

What is (x,y) rotated to when it undergoes a 180° rotation around the origin?

  • (-x,-y) (correct)
  • (-y,x)
  • (x,y)
  • (y,-x)

What is (4,-6) rotated 180 degrees?

<p>(-4,6)</p> Signup and view all the answers

Rotate (4,-6) 270 degrees clockwise.

<p>(6,4)</p> Signup and view all the answers

What does not change when you rotate a point, line, or figure?

<p>Shape or size</p> Signup and view all the answers

Rotating 180 degrees is the same as reflecting over what?

<p>both the x and y axis</p> Signup and view all the answers

Rotating (4,-6) 90 degrees clockwise puts the point where?

<p>(-6,-4)</p> Signup and view all the answers

How many 90 degree turns would 540 degrees be?

<p>6</p> Signup and view all the answers

180 degree rotation about the origin results in ___.

<p>(-x,-y)</p> Signup and view all the answers

Flashcards

90° CCW Rotation

After a 90 degree counter-clockwise rotation around the origin, a point (x, y) transforms into (-y, x).

90° CW Rotation

After a 90 degree clockwise rotation around the origin, a point (x, y) transforms into (y, -x).

180° Rotation

After a 180 degree rotation around the origin, a point (x, y) transforms into (-x, -y).

Rotation Invariance

Rotating a point, line, or figure doesn't change its shape or size. Only its position in the coordinate plane changes.

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180° Rotation and Reflection

Rotating a figure by 180 degrees around the origin is equivalent to reflecting the figure over both the x-axis and the y-axis.

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270° CW = 90° CCW

Rotating a point by 270 degrees clockwise is the same as rotating it 90 degrees counterclockwise.

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90° CW Rotation of (x,y)

Rotating a point (x, y) 90 degrees clockwise around the origin results in the point (y, -x).

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Equivalent Rotations

A 540 degree rotation around the origin is equivalent to six 90 degree rotations.

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180° Rotation Result

Rotating a point (x, y) 180 degrees around the origin results in the point (-x, -y).

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180° Rotation of (4,-6)

Rotating a point (4, -6) 180 degrees around the origin results in the point (-4, 6).

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Study Notes

Rotations on the Coordinate Plane

  • A 90° counterclockwise rotation of point (x,y) transforms it to (-y,x).
  • A 90° clockwise rotation of point (x,y) changes it to (y,-x).
  • A 180° rotation around the origin changes point (x,y) to (-x,-y).
  • The point (4,-6) rotated 180 degrees around the origin results in (-4,6).
  • Rotating point (4,-6) 270 degrees clockwise leads to the new position of (6,4).
  • The shape or size of a point, line, or figure remains unchanged during rotation.
  • A 180° rotation is equivalent to reflecting over both the x-axis and y-axis.
  • When (4,-6) is rotated 90 degrees clockwise, it moves to the position (-6,-4).
  • A rotation of 540 degrees equals six 90-degree rotations.
  • A 180-degree rotation around the origin has the effect of flipping a shape upside down.

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