shelby list the transformations in order using proper notation. (r, t, …

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…

Kategorie: geometry Aktualisiert: 2026-02-09

Aufgabe

shelby
list the transformations
in order using proper
notation. (r, t, r)

Lösungsschritte

Understand the question
shelby
list the transformations
in order using proper
notation. (r, t, r)
Explanation
Step1: Identify first transformation

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)

Step2: Identify second transformation

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

Step3: Identify third transformation

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: $R_{A'', -90^\circ}(\triangle A''B''C'') = \triangle A'''B'''C'''$
Final answer
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)
3. Rotation: $R_{A'', -90^\circ}(\triangle A''B''C'') = \triangle A'''B'''C'''$ (90° clockwise rotation about $A''$)
In order of application: $\boldsymbol{T
ightarrow r
ightarrow R}$

Antwort

Explanation

Step1: Identify first transformation

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)

Step2: Identify second transformation

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

Step3: Identify third transformation

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: $R_{A'', -90^\circ}(\triangle A''B''C'') = \triangle A'''B'''C'''$

Answer

Translation: $T_{(0, k)}(\triangle ABC) = \triangle A'B'C'$ (vertical downward shift)
Reflection: $r_{x=a}(\triangle A'B'C') = \triangle A''B''C''$ (vertical line reflection)
Rotation: $R_{A'', -90^\circ}(\triangle A''B''C'') = \triangle A'''B'''C'''$ (90° clockwise rotation about $A''$)

In order of application: $\boldsymbol{T
ightarrow r
ightarrow R}$

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Question Analysis

Subject mathematics

Sub Subject geometry

Education Level high school

Difficulty unspecified

Question Type with image

Multi Question No

Question Count 1

Analysis Status completed

Analyzed At 2026-02-09T20:32:17

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shelby
list the transformations
in order using proper
notation. (r, t, r)

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