1. Translation: $T_{(0, k)}(\triangle ABC) = \triangle A'B'C'$ (vertical downward shift) 2. Reflection: $r_{x=a}(\triangle A'B'C') = \triangle A''B''C''$ (vertical line reflection…
shelby
list the transformations
in order using proper
notation. (r, t, r)
shelby
list the transformations
in order using proper
notation. (r, t, r)
The first step is a translation ($T$) that maps $\triangle ABC$ to $\triangle A'B'C'$, shifting the triangle vertically downward.
Notation: $T_{(0, k)}(\triangle ABC) = \triangle A'B'C'$ where $k<0$ (negative vertical shift)
The second step is a reflection ($r$) that maps $\triangle A'B'C'$ to $\triangle A''B''C''$, flipping the triangle over a vertical line (preserving orientation of vertices relative to each other, matching the shape change).
Notation: $r_{x=a}(\triangle A'B'C') = \triangle A''B''C''$ where $a$ is the vertical reflection line
The third step is a rotation ($R$) that maps $\triangle A''B''C''$ to $\triangle A'''B'''C'''$, rotating the triangle 90 degrees clockwise around point $A''$ (matching the final rotated position).
Notation: $R_{A'', -90^\circ}(\triangle A''B''C'') = \triangle A'''B'''C'''$
In order of application: $\boldsymbol{T
ightarrow r
ightarrow R}$
The first step is a translation ($T$) that maps $\triangle ABC$ to $\triangle A'B'C'$, shifting the triangle vertically downward.
Notation: $T_{(0, k)}(\triangle ABC) = \triangle A'B'C'$ where $k<0$ (negative vertical shift)
The second step is a reflection ($r$) that maps $\triangle A'B'C'$ to $\triangle A''B''C''$, flipping the triangle over a vertical line (preserving orientation of vertices relative to each other, matching the shape change).
Notation: $r_{x=a}(\triangle A'B'C') = \triangle A''B''C''$ where $a$ is the vertical reflection line
The third step is a rotation ($R$) that maps $\triangle A''B''C''$ to $\triangle A'''B'''C'''$, rotating the triangle 90 degrees clockwise around point $A''$ (matching the final rotated position).
Notation: $R_{A'', -90^\circ}(\triangle A''B''C'') = \triangle A'''B'''C'''$
In order of application: $\boldsymbol{T
ightarrow r
ightarrow R}$
shelby list the transformations in order using proper notation. (r, t, r)
Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806
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