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Transformations

The Hook

Shapeshifting.

What is it?

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

Time Travel (History)

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

Cheat Code

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

Practice This Now!

The Field Guide

In 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.

In The Real World: 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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Booby Trap!

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

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

Training Drills

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