Transformations in Geometry Flashcards

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Questions and Answers

What is the translation formula (x,y) ~ ?

  • (-x,y)
  • (x-4,y+7) (correct)
  • (2x,2y)
  • (y,-x)

What does the reflection formula y=x represent?

(x,y) ~ (y,x)

How is a point reflected over the y-axis?

(x,y) ~ (-x,y)

How is a point reflected over the x-axis?

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

What is the dilation formula for a scale factor of 2?

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

What is the rotation formula for 90 degrees counterclockwise?

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

What is the rotation formula for 180 degrees?

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

What is the rotation formula for 270 degrees clockwise?

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

What does vertical reflection mean?

<p>Reflection over x axis</p> Signup and view all the answers

What does horizontal reflection mean?

<p>Reflection over y axis</p> Signup and view all the answers

What is the vertical reflection formula?

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

What is the horizontal reflection formula?

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

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Study Notes

Translation

  • Transformation that shifts a figure horizontally and vertically.
  • Formula: (x, y) ~ (x-4, y+7) indicates a left movement of 4 units and an upward movement of 7 units.

Reflection

  • Reflection over the line y = x swaps the coordinates of a point.
  • Formula: (x, y) ~ (y, x).

Reflection over the y-axis

  • Flips the figure over the y-axis, changing the sign of the x-coordinate.
  • Formula: (x, y) ~ (-x, y).

Reflection over the x-axis

  • Flips the figure over the x-axis, changing the sign of the y-coordinate.
  • Formula: (x, y) ~ (x, -y).

Dilation

  • A transformation that alters the size of a figure by a scale factor.
  • Example: Dilation by a scale factor of 2 is represented as (x, y) ~ (2x, 2y).

Rotation 90 degrees counterclockwise

  • Changes the position of a point by rotating it 90 degrees in the counterclockwise direction.
  • Formula: (-y, x).

Rotation 180 degrees

  • Rotates a point to the opposite quadrant.
  • Formula: (-x, -y).

Rotation 270 degrees

  • Rotates a point 270 degrees counterclockwise, which is equivalent to a 90-degree clockwise rotation.
  • Formula: (y, -x).

Vertical reflection

  • Another term for reflection over the x-axis.
  • The property causes flipping across the horizontal axis.

Horizontal reflection

  • Refers to reflection over the y-axis.
  • The property results in flipping across the vertical axis.

Vertical reflection formula

  • Represents the transformation of a function across the x-axis.
  • Formula: y = -f(x).

Horizontal reflection formula

  • Represents the transformation of a function across the y-axis.
  • Formula: y = f(-x).

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