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4.A: Reflections and Translations

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)


    The purpose of this lesson is to learn how to represent reflections and translations on the coordinate plane.

    This lesson will address the following CCRS Standard(s) for Geometry:

    • 8.G.2: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them


    1. Take notes while watching videos below
    2. Go to and log into our course to complete assignment 4.A with 80% or better.


    Complete assignment 4.A with 80% or better at


    In this lesson we have learned:

    • Reflections create a mirror image of the original shape which is congruent to the original shape
      • Reflecting (a,b) over the x-axis gives the point (a,-b)
      • Reflecting (a,b) over the y-axis gives the point (-a,b)
      • Reflecting (a,b) over the origin gives the point (-a,-b)
      • Reflecting (a,b) over the line y=x gives the point (b,a)
    • Translations slide the original shape creating a second congruent shape
      • Translating (a,b) up c and right d units gives (a+d,b+c)

    4.A: Reflections and Translations is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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