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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…

分类: geometry 更新时间: 2026-02-09

题目

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

解题步骤

  1. Understand the question

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

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

  3. 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: $\boldsymbol{T
    ightarrow r
    ightarrow R}$

答案

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

  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: $\boldsymbol{T
ightarrow r
ightarrow R}$

Question Image

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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

OCR Text

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

相关知识点

mathematicsgeometrywith imagehigh schoolturns-1

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