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Dilations with Different Scale Factors

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About This Diagram

This diagram shows how dilations change the size of a figure while preserving its shape. Click different scale factors to see enlargements and reductions.

Scale Factor Effects

Scale Factor Effect Example
k > 1 Enlargement k = 2 doubles size
k = 1 No change Identity
0 < k < 1 Reduction k = 0.5 halves size

Visual Elements

  • Red dot: Center of dilation
  • Blue triangle: Pre-image
  • Green triangle: Image (dilated)
  • Dashed lines: Radial lines from center through vertices
  • Distance labels: Show proportional changes

Key Concepts

  • All points move along lines through the center
  • Distances are multiplied by scale factor k
  • Shape is preserved, but size changes
  • Dilations are NOT rigid motions!

Coordinate Rule

(x, y) → (kx, ky) when center is at origin

Interaction

Click "k = 2", "k = 0.5", or "k = 1.5" to animate each dilation.

Learning Objectives

  • Understand how scale factor affects size
  • Apply dilation rules to coordinates

Bloom's Taxonomy Level

Understanding and Applying - Visualizing dilations.

Iframe Embed Code

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