Teacher Version
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." [EX1, page 4]
Transformation
Triangle produced
Reflection across the x-axis
Triangle 4
Translation down 6 units and left 8 units
Triangle 3
Rotation 180° about the origin
No triangle
Reflection across the y-axis
Triangle 2
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Page 3 of 7
Teacher Version
Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
Use the diagram below to answer questions 5-9.
5. P' is a reflection of P across line m. What must be true about PM and P'M ?
[EX1, page 6]
PM and P'M are congruent.
6. What appears to be true about ∠PMA and ∠P'MA ? [EX1, page 6]
∠PMA and ∠P'MA are both right angles.
7. What does the conclusion you reached in question 5 tell you about line m and P'P ?
[EX1, page 6]
From this information, one can conclude that line m is the perpendicular bisector of
P'P .
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Page 4 of 7
Teacher Version
Rigid transformations
Student Activity Sheet 2; use with Exploring “Translations and reflections”
8. Define the reflection of point P across line m. [EX1, page 7]
Point P' is the reflection across line m of point P if line m is the perpendicular
bisector of P'P .
9. REINFORCE PM = (3x – 5) millimeters and P'M = (x2 – 5) millimeters. Find PP'.
Since M lies on the line of reflection, PM = P'M.
3x – 5 =
3x =
2
x – 3x =
x(x – 3) =
x = 0 and
x2 – 5
x2
0
0
x=3
If x = 0, then PM = -5 mm, which cannot be true.
So, x = 3 and PM = P'M = (3(3) – 5) mm = 4 mm.
PP' = PM + P'M = 4 mm + 4 mm = 8 mm.
Copyright 2015 Agile Mind, Inc. ®
Content copyright 2015 Charles A. Dana
Center, The University of Texas at Austin
Page 5 of 7