Geometry: Reflection and Rotation Rules

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Questions and Answers

What is the result of reflecting a point over the x-axis?

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

What is the result of reflecting a point over the y-axis?

(-x, y)

What does reflecting over the line y = x result in?

(y, x)

What is the result of reflecting a point over the line y = -x?

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

What is the result of reflecting a point through the origin?

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

What is the rule for a 90 degree counterclockwise rotation?

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

What happens during a 180 degree rotation?

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

What is the result of a 270 degree counterclockwise rotation?

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

What is the rule for a 90 degree clockwise rotation?

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

What is the result of a 360 degree rotation?

<p>Stays where it is</p> Signup and view all the answers

What is the rule for a larger than 360 degree rotation?

<p>Subtract 360 from the amount and use the leftover to figure the rule</p> Signup and view all the answers

What is the rule for a 270 degree clockwise rotation?

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

What is translation in terms of coordinate transformations?

<p>(x+1, y-2)</p> Signup and view all the answers

What does dilation refer to in transformations?

<p>(2x, 3y)</p> Signup and view all the answers

What is rigid motion?

<p>The figure preserves size and shape.</p> Signup and view all the answers

What are the three transformations that are rigid?

<p>Reflection, translation, rotation</p> Signup and view all the answers

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Study Notes

Reflection Rules

  • Reflecting over the x-axis transforms a point (x, y) to (x, -y).
  • Reflecting over the y-axis changes a point (x, y) to (-x, y).
  • Reflecting over the line y = x swaps coordinates, resulting in (y, x).
  • Reflecting over the line y = -x transforms the point to (-y, -x).
  • Reflecting through the origin changes (x, y) to (-x, -y).

Rotation Rules

  • A 90-degree counterclockwise rotation transforms (x, y) to (-y, x).
  • A 180-degree rotation changes the coordinates by negating both, translating (x, y) to (-x, -y).
  • A 270-degree counterclockwise rotation results in (y, -x).
  • A 90-degree clockwise rotation has the same effect as a 270-degree counterclockwise rotation, yielding (y, -x).
  • A 360-degree rotation leaves the point unchanged.
  • For a rotation larger than 360 degrees, subtract 360 degrees from the angle to find the equivalent transformation.
  • A 270-degree clockwise rotation matches a 90-degree counterclockwise rotation, transforming (x, y) to (-y, x).

Translation and Dilation Rules

  • Translation involves adding or subtracting values, which results in sliding the object; it shifts a point (x, y) to (x+1, y-2).
  • Dilation relates to multiplication or division, which alters the size of the object, changing (x, y) to (2x, 3y).

Rigid Motion

  • Rigid motion preserves both the size and shape of the figure.
  • The three transformations classified as rigid motions include reflection, translation, and rotation.

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