Composition of Transformations

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About This MicroSim

This interactive tool lets you explore compositions of transformations by selecting T₁ and T₂, then watching the figure transform in sequence.

How to Use

1. Select T₁ (first transformation) from Translation, Rotation, or Reflection
2. Select T₂ (second transformation)
3. Click "Animate" to watch the composition step-by-step
4. Click "Reset" to start over

Composition Notation

T₂ ∘ T₁ means "Apply T₁ first, then T₂"

Visual Stages

Color	Stage
Blue	Original figure
Purple	After T₁
Green	After T₂ (Final result)

Key Concepts

• Order matters! T₂ ∘ T₁ ≠ T₁ ∘ T₂ in most cases
• Composition of rigid motions produces a rigid motion
• Two reflections over parallel lines = translation
• Two reflections over intersecting lines = rotation

Learning Objectives

• Apply sequences of transformations
• Analyze how order affects the result
• Create specific compositions to achieve desired transformations

Bloom's Taxonomy Level

Applying, Analyzing, and Creating - Multi-stage transformations.

Iframe Embed Code

<iframe src="https://dmccreary.github.io/geometry-course/sims/composition-transformations/main.html"
        height="602px"
        width="100%"
        scrolling="no"></iframe>