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Rigid Transformations

Perform translations, reflections, and rotations on the coordinate plane.

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Rigid Transformations

What Are Rigid Transformations?

Transformations that preserve size and shape (distances and angles stay the same). Also called isometries.

Translations (Slides)

Every point moves the same distance in the same direction.

(x,y)→(x+a,y+b)(x, y) \to (x + a, y + b)

Example: Translate by ⟨3,−2⟩\langle 3, -2 \rangle: (1,4)→(4,2)(1, 4) \to (4, 2)

Reflections (Flips)

Every point is mirrored across a line of reflection.

Reflection OverRule
x-axis(x,y)→(x,−y)(x, y) \to (x, -y)
y-axis(x,y)→(−x,y)(x, y) \to (-x, y)
y=xy = x(x,y)→(y,x)(x, y) \to (y, x)
y=−xy = -x(x,y)→(−y,−x)(x, y) \to (-y, -x)

Rotations (Turns)

Rotating about the origin counterclockwise:

AngleRule
90°90°(x,y)→(−y,x)(x, y) \to (-y, x)
180°180°(x,y)→(−x,−y)(x, y) \to (-x, -y)
270°270°(x,y)→(y,−x)(x, y) \to (y, -x)

Congruence Through Transformations

Two figures are congruent if one can be mapped to the other using a sequence of rigid transformations.

△ABC≅△DEF\triangle ABC \cong \triangle DEF

means there exists a combination of translations, reflections, and/or rotations that maps △ABC\triangle ABC exactly onto △DEF\triangle DEF.

Key principle: Rigid transformations preserve distances, angle measures, and parallelism.

Explain using:
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Triangle Congruence Theorems
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📌 Related Topics in Transformations and Congruence

Triangle Congruence TheoremsTranslationReflectionRotation

❓ Frequently Asked Questions

What is Rigid Transformations?▾
Perform translations, reflections, and rotations on the coordinate plane.
How can I study Rigid Transformations effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Regular review and active practice are key to retention.
Is this Rigid Transformations study guide free?▾
Yes — all study notes, flashcards, and practice problems for Rigid Transformations on Study Mondo are free to access. No account is needed.
What course covers Rigid Transformations?▾
Rigid Transformations is part of the Geometry course on Study Mondo, specifically in the Transformations and Congruence section. You can explore the full course for more related topics and practice resources.