Mathematics
Grade 7
15 min
Identify reflections, rotations, and translations
Identify reflections, rotations, and translations
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1
Introduction & Learning Objectives
Learning Objectives
Define and differentiate between reflections, rotations, and translations.
Visually identify a reflection given a pre-image and its image.
Visually identify a rotation given a pre-image and its image.
Visually identify a translation given a pre-image and its image.
Explain the key characteristics that distinguish each type of transformation.
Recognize that reflections, rotations, and translations preserve congruence.
Apply their understanding to identify transformations in simple geometric figures.
Have you ever looked in a mirror and seen your reflection? Or watched a Ferris wheel turn? 🎡 These are everyday examples of how shapes move in geometry!
In this lesson, we'll explore three fundamental ways to move shapes without changing their size or...
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Key Concepts & Vocabulary
TermDefinitionExample
TransformationA mathematical operation that moves or changes a geometric figure in some way to produce a new figure.Moving a square from one corner of a grid to another is a transformation.
Pre-imageThe original figure before a transformation is applied.If you start with triangle ABC, it is the pre-image.
ImageThe new figure that results from a transformation of the pre-image. It is often denoted with prime symbols (e.g., A'B'C').After moving triangle ABC, the new triangle A'B'C' is the image.
ReflectionA transformation that 'flips' a figure over a line, creating a mirror image. The line is called the line of reflection.Flipping a letter 'P' across a vertical line to make a backward 'P'.
RotationA transforma...
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Core Formulas
Rule for Identifying a Translation (Slide)
$ ext{If the image has moved without changing its orientation or being flipped, it is a translation.}$
Look for a simple shift in position. All points on the figure move the same distance in the same direction. The figure looks exactly the same, just in a different spot.
Rule for Identifying a Reflection (Flip)
$ ext{If the image is a mirror image of the pre-image across a line, it is a reflection.}$
Check if the figure appears 'flipped' or reversed. The orientation of the figure will be opposite to the pre-image (e.g., if the pre-image reads 'P', the image might look like a backward 'P').
Rule for Identifying a Rotation (Turn)
$ ext{If the image appears to have turned around a fixed point, it is...
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Challenging
A triangle is first translated 2 units up, and then reflected across the y-axis. Which of the following describes the final image compared to the pre-image?
A.The image is congruent but has a different location and orientation.
B.The image is a different size.
C.The image has the same location but a different orientation.
D.The image has the same orientation but a different location.
Challenging
The image of a square, A'B'C'D', was created by translating the pre-image 4 units left and 1 unit up. If vertex A' is at (2, 5), what were the coordinates of the original vertex A?
A.(-2, 6)
B.(6, 6)
C.(6, 4)
D.(-2, 4)
Challenging
Which statement is ALWAYS true for a reflection but NOT ALWAYS true for a rotation?
A.The image is congruent to the pre-image.
B.The orientation of the vertices (e.g., from clockwise to counter-clockwise) is reversed.
C.Every point on the pre-image moves to a new location.
D.The transformation is described by a single point.
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