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

    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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    Description

    Test your knowledge of geometric transformations with these flashcards. This quiz covers translation, reflection, dilation, and rotation formulas with definitions and examples. Perfect for students studying geometry.

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