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14.2: Reflect a Figure
Your classmate says that Triangle \(2\) is the image of Triangle \(1\) under a reflection in the line \(y = x\). Give \(2\) reasons why Triangle \(2\) is not the image of Triangle \(1\). Write down the steps to help your classmate graph the correct image. Use at least \(3\) sentences and \(3\) vocabulary terms.

Key Vocabulary

line of reflection
equal distance
opposite sides
perpendicular bisector
  • \(\triangle 2\) is not the reflection of \(\triangle 1\) because:

       - The two triangles are not congruent.
       - The triangles are not equal distances from the line of reflection.

    Steps to draw the correct image:

    1) Draw a perpendicular line from \(A\) to the line of reflection and extend the line beyond the line
       of reflection.
    2) Measure the distance from \(A\) to the line of reflection. \(A’\) will be the same distance on the     other side of the line of reflection.
    3) To find \(B’\) and \(C’\), repeat steps \(1\) and \(2\) for \(B\) and \(C\).
    4) Join the vertices of \(A’\), \(B’\) and \(C’\) to draw the image.
  • Think of the properties of reflections.
  • What do you know about the size of a figure and its reflection?
  • What can you say about the distance of a figure and its reflection from the line of reflection?