Geometric Transformations
Master rigid and non-rigid 2D coordinate mappings. Explore translations, rotational turns, axis reflections, and origin dilations visually.
Interactive Grid
Transformational Canvas
A geometric transformation maps points of a pre-image shape to new positions on the coordinate plane. Select a mapping type, slide variables, and trace the pre-image A transitioning to image A'.
Coordinate Mapping Rule
(x, y) → (x + 3, y - 2)
Shape Presets:
Vertex Transformations mapping:
A(1, 2) → A'(4, 0)
Anatomy Specs
Transformation Principles
Review the structural mathematical mappings behind each 2D transformation category.
Mapping Functions Matrix
Translation (Rigid):
Shifts all coordinates uniformly. Preserves size, angles, and orientation.
x' = x + dx, y' = y + dy
x' = x + dx, y' = y + dy
Rotation (Rigid):
Spins points around origin (0,0) by angle θ. Preserves size and angles.
x' = x·cos(θ) - y·sin(θ), y' = x·sin(θ) + y·cos(θ)
x' = x·cos(θ) - y·sin(θ), y' = x·sin(θ) + y·cos(θ)
Reflection (Rigid):
Flips shape across an axis line. Preserves size/angles; reverses orientation.
Across x-axis: (x, -y) | Across y-axis: (-x, y) | Across y=x: (y, x)
Across x-axis: (x, -y) | Across y-axis: (-x, y) | Across y=x: (y, x)
Dilation (Non-Rigid / Similarity):
Scales shape from origin (0,0) by scale s. Changes size; preserves angles/proportions.
x' = s·x, y' = s·y
x' = s·x, y' = s·y
Orientation & Congruence
Congruent Transformations:
Translations, rotations, and reflections produce images congruent to the pre-image (identical lengths and shapes).
Similar Transformations:
Dilations scale dimensions, producing similar shapes (angles remain equal, sides map to scale factor ratio).
Orientation:
Reflections flip the orientation of the shape (vertices go from counter-clockwise to clockwise order).
Self Evaluation
Transformation Quiz
Evaluate your core understanding of coordinate mappings, matrices, and rigid motion rules.
Question 1 of 5
Score: 0/0
Which of the following is a NON-RIGID transformation that alters the size of the shape?
Correct Answer!
Explanation goes here.
Focus Area Vocabulary
- Pre-Image: Original shape (A)
- Image: Mapped shape (A')
- Rigid Motion: Preserves shape & sizes