Overview
Watch
Read
Next Steps
Overview
Precalculus
31. CC.HSN.VM.C.12
31.1 Finding the transformation matrix
Finding the Transformation Matrix
A transformation matrix moves or reshapes figures on the plane; find it from where the basis vectors are sent.
What You'll Learn
A transformation matrix maps every point of a figure to a new position.
Apply it by multiplying the matrix by a point's coordinate vector.
To find it, see where the basis vectors (1,0) and (0,1) are sent.
Those two images become the columns of the matrix.
The identity matrix, with ones on the diagonal, leaves points unchanged.
What You'll Practice
1
Finding transformed vectors from scaling, rotation, and reflection descriptions
2
Determining transformation matrices from graphical representations
3
Applying reflections across x-axis, y-axis, and y=x line to unit vectors
4
Converting rotation angles (90°, 270° clockwise/counterclockwise) into matrix form
Why This Matters
Understanding how to find transformation matrices is essential for computer graphics, robotics, and physics. This skill lets you encode any geometric transformation as a matrix, which is fundamental in animation, game development, and engineering applications where objects move and rotate in space.
Before You Start — Make Sure You Can:
This Unit Includes
11 Video lessons
Learning resources
Skills
Transformation Matrices
Unit Vectors
Reflections
Rotations
Scaling
Linear Transformations
Matrix Construction
IL Curriculum Aligned