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Predicting Results of Rigid Transformations
The Lesson Activities will help you meet these educational goals:
Content Knowledge— You will predict the result of a rigid transformation and specify a
sequence of transformations to carry a given figure onto another.
Mathematical Practices—You will make sense of problems and solve them, reason
abstractly and quantitatively, and use mathematics to model realworld situations.
STEM—You will apply mathematical tools and knowledge to grow in your understanding
of mathematics as a creative human activity.
Directions
You will evaluate some of these activities yourself, and your teacher may evaluate others.
Please save this document before beginning the lesson and
keep the document open for
reference
during the lesson. Type your answers directly in this document for all activities.
_________________________________________________________________________
SelfChecked Activities
Read the instructions for the following activities and type in your responses. At the end of the
lesson, click the link to open the Student Answer Sheet. Use the answers or sample
responses to evaluate your own work.
1.
Results of Single Transformations
Use GeoGebra to predict the results of a
single transformation
and complete each step
below. If you need help, follow these
instructions
for using GeoGebra.
a.
First you will examine how reflections affect the orientation and
location of quadrilateral
ABCD
on the coordinate plane.
1.
Predict what will happen to the coordinates of a point (
x
,
y
) as the point
reflects across a line to produce point (
x
′,
y
′). Choose the
x
axis,
y
axis,
y
=
x
, and
y
= 
x
for the lines of reflection. Express your answers in terms of
x
and
y
. (Be sure
to watch your signs.)
Type your response here:
Line of reflection
x
′
y
′
x
axis
y
axis
y = x
y = x
1
Geometry
Lesson Activities
2.
Enter the numerical coordinates of the vertices of quadrilateral
ABCD
in the
table. (Point
A
has been done for you.) Then predict the numerical coordinates of
the vertices of quadrilateral
A
′
B
′
C
′
D
′ as the figure reflects about four different lines
of reflection:
x
axis,
y
axis,
y
=
x
, and
y
= 
x
.
Type your response here
:
A
B
C
D
(3, 2)
Line of reflection
A
′
B
′
C
′
D
′
x
axis
y
axis
y = x
y = x
3.
Now check your predictions. In GeoGebra, draw the lines of reflection
y = x
and
y
= x
. Then reflect quadrilateral
ABCD
about the
x
axis,
y
axis,
y
=
x
, and
y
=

x
. Enter the coordinates of the vertices of quadrilateral
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 Fall '17
 ms wessel
 Geometry, Transformations, Cartesian Coordinate System, René Descartes, Polar coordinate system