2D Transformation Matrices

Vocabulary flashcards covering common 2D transformation matrices including reflections, rotations, identity, and dilation.

Identity Matrix (No Change)

The matrix representing no change to a geometric figure, given by $\begin{bmatrix} 1 & 0 ; 0 & 1 \end{bmatrix}$.

Reflection over the x-axis ($r_x$)

The transformation matrix for a reflection across the x-axis, given by $r_x = \begin{bmatrix} 1 & 0 ; 0 & -1 \end{bmatrix}$.

Reflection over the y-axis ($r_y$)

The transformation matrix for a reflection across the y-axis, given by $r_y = \begin{bmatrix} -1 & 0 ; 0 & 1 \end{bmatrix}$.

Reflection over the line $y = x$

The transformation matrix for a reflection across the line $y = x$, given by $\begin{bmatrix} 0 & 1 ; 1 & 0 \end{bmatrix}$.

Reflection over the line $y = -x$ ($r_{y=-x}$)

The transformation matrix for a reflection across the line $y = -x$, given by $r_{y=-x} = \begin{bmatrix} 0 & -1 ; -1 & 0 \end{bmatrix}$.

$90^\circ$ Rotation ($R_{90^\circ}$)

The transformation matrix representing a $90^\circ$ rotation, given by $R_{90^\circ} = \begin{bmatrix} 0 & -1 ; 1 & 0 \end{bmatrix}$.

$180^\circ$ Rotation

The transformation matrix representing a $180^\circ$ rotation, given by $\begin{bmatrix} -1 & 0 ; 0 & -1 \end{bmatrix}$.

$270^\circ$ Rotation ($R_{270^\circ}$)

The transformation matrix representing a $270^\circ$ rotation, given by $R_{270^\circ} = \begin{bmatrix} 0 & 1 ; -1 & 0 \end{bmatrix}$.

Dilation ($D_k$)

The transformation matrix representing a dilation with scale factor $k$, given by $D_k = \begin{bmatrix} k & 0 ; 0 & k \end{bmatrix}$.

2D Transformation Matrix Reference Chart

A reference table outlining standard transformation matrices for identity, axis and line reflections, rotation angles ($90^\circ$, $180^\circ$, $270^\circ$), and dilation.