Student:
Class:
Date:
Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
1. Use the reflection of a point across a line to locate point C, the best place to connect A
and B so that the distance AB + BC is minimized.
2. Since C minimizes the distance from A to B', it also minimizes the distance from A to B.
Why is this true?
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
3. R
REEIINNFFOORRCCEE The diagram shows a miniature golf hole. Starting at the tee, construct a
path that would result in a hole-in-one. Explain your solution.
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Student:
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Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
4. Triangle 5 is the pre-image of a transformation or series of transformations. For each of
the transformations or series of transformations in the table, identify which triangle is
the image of triangle 5 that is produced by that transformation. If the transformation
does not produce any of the triangles shown, then write "No triangle."
Transformation
Triangle produced
Reflection across the x-axis
Translation down 6 units and left 8 units
Rotation
about the origin
Reflection across the y-axis
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
Use the diagram below to answer questions 4-8.
5. P' is a reflection of P across line m. What must be true about
6. What appears to be true about
and
and
?
?
7. What does the conclusion you reached in question 5 tell you about line m and
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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?
Student:
Class:
Date:
Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
8. Define the reflection of point P across line m.
9. R
REEIINNFFOORRCCEE PM = (3x – 5) millimeters and PM' = (x2 – 5) millimeters. Find PP'.
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
Triangle A''B''C'' is the composition of two reflections of ∆ABC across m1 and m2. Using
this information and the diagram below, answer questions 9-13.
10. How do the size and shape of
compare with those of
?
11. What do your measurements tell you about the reflected images A", B", and C" of the
vertices A, B, and C?
12. How does the fixed distance between pre-images A, B, and C and images A", B" and C"
compare with the distance between the parallel lines?
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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Student:
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Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
13. Fill in the blanks to complete the following statement.
A translation of a shape is a composition of two
across
lines.
14.R
REEIINNFFOORRCCEE In the diagram on the previous page, AA'' = (3x – 9) millimeters and the
distance between lines m1 and m2 is 6 millimeters. Solve for x.
Copyright 2012 Agile Mind, Inc. ®
Content copyright 2012 Charles A. Dana
Center, The University of Texas at Austin
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