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Transformations

Overview

Shapeshifting.

What is it?

Operations that move or resize a shape: Translation (Slide), Reflection (Flip), Rotation (Turn), Dilation (Zoom).

History

The math of symmetry used in tiling patterns (tessellations) in ancient Islamic architecture.

Key Idea

Slide = Add/Sub. Flip = Negate one coord. Zoom = Multiply.

Practice This Topic

Concept Guide

Plain English: Take a shape and move it. If you just slide, turn, or flip it, it stays the same size (Rigid). If you stretch or shrink it (Dilation), the size changes but the angles stay the same.

Real-world example: Computer Graphics (CGI). To move a 3D model, the computer applies a 'Transformation Matrix' to every vertex of the character.

How to do it

  1. Identify the type of move.
  2. Translation: Add (a, b) to every (x, y).
  3. Reflection X-axis: Change (x, y) to (x, -y).
  4. Dilation: Multiply (x, y) by scale factor k.
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Common Pitfall

Rotation Direction. Positive degrees usually mean Counter-Clockwise. Negative means Clockwise.

Word Problem
"A triangle has a corner at (2,3). You translate it 4 units right and 2 units down. Where is the corner now?"
Reasoning: Right 4 means x+4. Down 2 means y-2. (2+4, 3-2) = (6, 1).

Practice Examples

Reflection
| / | / ---+--- | \ | \
Flipped over the x-axis.