Reflections

Vocabulary

• A rigid motion is a transformation that preserves length and angle measurement.
• A reflection is a flip over a line called the line of reflection. Each point and its image are the same distance from the line of reflection.
• Possible lines of reflection: x-axis, y-axis, vertical or horizontal lines in the form x=# or y = #, diagonal lines in the form y=x or y=-x.

Example

• Reflect AABC across the x-axis:

  • A(-4,2) becomes A'(-4,-2)
  • B(4,7) becomes B'(4,-7)
  • C(5,1) becomes C'(5,-1)

• Reflect PARS across the y-axis:

  • P(1,2) becomes P'(-1,2)
  • Q(2,5) becomes Q'(-2,5)
  • R(8,3) becomes R'(-8,3)
  • S(7,0) becomes S'(-7,0)

Reflection over y=x line

• It involves switching the places of the x and y coordinates.

Understanding Reflection and Translation in Geometry Answer Key

Translation

• Translation is to vertically and/or horizontally slide a figure.
• Symbolic form: (x,y) → (x+h, y+k) or
• h represents the horizontal shift and k represents the vertical shift.

Example

• Original points:
  • Q(-6,1), R(-3,1), T(-2,-7), S(1,-5)
• Translation rule:
  • (x,y) → (x+5, y+1) or <5,1>
• New points:
  • Q'(-1,6), R'(2,18), T'(3,0), S'(6,2)

Composition of Rigid Motion

• It involves a transformation with two or more rigid motions in which the second rigid motion is performed on the image of the first rigid motion.

Example

• 3 reflections across the x-axis and T(4,9)
• New points: X''(6,-8), Y''(7,-2), Z''(4,-3)

Reflection, Rotation, and Translation in Geometry PDF

Rotations

• Rules:
  • 90° rotation: (x,y) → (-y, x)
  • 180° rotation: (x,y) → (-x, -y)
  • 270° rotation: (x,y) → (y, -x)

Example

• Rotate 90° about the origin:

  • A(3,5) becomes A'(-5,3)
  • B(1,7) becomes B'(-7,1)
  • C(-2,4) becomes C'(-4,-2)
  • D(2,-1) becomes D'(1,2)

• Rotating around a point:

  1. Write your original points.
  2. Subtract the point of rotation from the original points.
  3. Use rotation rules to find new points.
  4. Add back the point of rotation to new points.

Translations, Reflections, and Rotations Worksheet

Non-Rigid Motion

• It includes translation, rotation, and reflection in geometry.
• Non-rigid motion does not preserve length and angle measurement.

Rigid Motion in Geometry Formulas

• Rigid motion in geometry is defined by specific formulas that preserve length and angle measurement.

Types of Rigid Motion in Geometry

• Rigid motion in geometry includes translations, reflections, and rotations.

This understanding reflection and translation in geometry worksheet provides a comprehensive overview of reflections, translations, and rotations in geometry, including examples and rules for each type of rigid motion. The answer key is also provided to assist in understanding the concepts. For more in-depth information, the Understanding Reflection and Translation in Geometry PDF is available for further study and practice.