📐 Geometry Transformations — Quick
Guide
🔵 What is a Transformation?
A transformation changes the position, size, or orientation of a shape on a coordinate plane.
🟢 RIGID TRANSFORMATIONS
(Shape stays the SAME size and shape)
➡️ 1. Translation (Slide)
Definition:
A translation slides a shape without turning or resizing it.
Key Idea:
Every point moves the same distance and direction
Example:
(x, y) → (x + 3, y − 2)
👉 Right 3, Down 2
🔄 2. Rotation (Turn)
Definition:
A rotation turns a shape around a fixed point (usually the origin).
Key Idea:
Angle + direction matter (clockwise or counterclockwise)
Common Rotations:
● 90° → (x, y) → (−y, x)
● 180° → (x, y) → (−x, −y)
🪞 3. Reflection (Flip)
, Definition:
A reflection flips a shape over a line (mirror line).
Key Idea:
Distance from the line stays the same
Examples:
● Over x-axis → (x, y) → (x, −y)
● Over y-axis → (x, y) → (−x, y)
🔴 NON-RIGID TRANSFORMATION
(Shape changes size)
🔍 4. Dilation (Resize)
Definition:
A dilation resizes a shape using a scale factor.
Key Idea:
Shape stays the same, but size changes
Examples:
● Scale factor 2 → bigger
● Scale factor ½ → smaller
(x, y) → (2x, 2y)
🧠 KEY VOCAB
● Rigid transformation → same size + shape
● Translation → slide
● Rotation → turn
● Reflection → flip
● Dilation → resize
● Scale factor → how much bigger/smaller
Guide
🔵 What is a Transformation?
A transformation changes the position, size, or orientation of a shape on a coordinate plane.
🟢 RIGID TRANSFORMATIONS
(Shape stays the SAME size and shape)
➡️ 1. Translation (Slide)
Definition:
A translation slides a shape without turning or resizing it.
Key Idea:
Every point moves the same distance and direction
Example:
(x, y) → (x + 3, y − 2)
👉 Right 3, Down 2
🔄 2. Rotation (Turn)
Definition:
A rotation turns a shape around a fixed point (usually the origin).
Key Idea:
Angle + direction matter (clockwise or counterclockwise)
Common Rotations:
● 90° → (x, y) → (−y, x)
● 180° → (x, y) → (−x, −y)
🪞 3. Reflection (Flip)
, Definition:
A reflection flips a shape over a line (mirror line).
Key Idea:
Distance from the line stays the same
Examples:
● Over x-axis → (x, y) → (x, −y)
● Over y-axis → (x, y) → (−x, y)
🔴 NON-RIGID TRANSFORMATION
(Shape changes size)
🔍 4. Dilation (Resize)
Definition:
A dilation resizes a shape using a scale factor.
Key Idea:
Shape stays the same, but size changes
Examples:
● Scale factor 2 → bigger
● Scale factor ½ → smaller
(x, y) → (2x, 2y)
🧠 KEY VOCAB
● Rigid transformation → same size + shape
● Translation → slide
● Rotation → turn
● Reflection → flip
● Dilation → resize
● Scale factor → how much bigger/smaller
