Transcript Problem 2.1 Symmetry Transformations

Problem 2.1
Symmetry Transformations
Transformations produce a copy of a figure in a
new position. The copy is called the image of the
original figure.
A'
A
j
B
B'
C
C'
D
E
These
points are
labeled as
A Prime,
B Prime,
C Prime,
D Prime
&
E Prime
D'
E'
Draw a line segment from each
vertex of polygon ABCDE to its
image on A’B’C’D’E’.
A’
A
B
B’
C’
C
D
E
D’
E’
1. Draw a line segment from each
vertex of polygon ABCDE to its
image on A’B’C’D’E’.
A’
A
B
B’
C’
C
D
E
D’
E’
2. Measure the angle formed by each
segment you drew and the line of
reflection.
These
angles:
A’
A
B
B’
C’
C
D
E
D’
E’
Check
your answers:
2. Measure
the angle
formed by each
segment
you
drew
and
the
line
of
Each line should be perpendicular to the line of
reflection.
reflection. They should make right (90º) angles.
These
angles:
A’
A
B
B’
C’
C
D
E
D’
E’
3. Measure the distance from the vertex to the line of
reflection along the segment you drew and the distance
from the line of reflection to the image of the vertex.
These
distances:
A’
A
B
B’
C’
C
D
E
D’
E’
Check your answers:
3.
Each matching measurement should be equal.
These
distances:
A’
A
B
B’
C’
C
D
E
D’
E’
4. Describe the patterns in your measurements from
parts 2 & 3. What did you notice about the measure
of the angles formed by the line of reflection? What
did you notice about the lengths from the vertices to
the line of reflection?
A’
A
B
B’
C’
C
D
E
D’
E’
Make sure each matching measurement is equal.
Make sure the line that connects image points is perpendicular to the line
4
of reflection.
A’
A
B
B’
C’
C
D
E
D’
E’
B. Use what you discovered in A to draw
the image of the polygon reflected over the
line. Describe how you drew your image.
J
N
K
M
L
B. Use what you discovered in A to draw
the image of the polygon reflected over the
line. Describe how you drew your image.
L’
K’
J’
M’
J
N’
N
K
M
L
Make sure each matching measurement is equal.
B. Use what you discovered in A to draw
Make sure the line that connects image points is perpendicular to the line
the image of the polygon
of reflection.reflected over the
line. Describe how you drew your image.
Make sure you label the correct image point to the correct vertex point.
L’
K’
J’
M’
J
N’
N
K
M
L
C. Use the designs to find the line
of reflection.
C. Use the designs to find the line
of reflection.
Find the line of reflection that will:
C.
Use
the
designs
to
find
the
line
be equidistance between original and image points.
of reflection.
be perpendicular to each segment that connects
original & image points.
2.1 Follow up # 2
Design 1
Go to
SketchPad
a) Draw the image
of the shape under
a reflection over
the line.
b) Does the final
drawing have
reflectional
symmetry?
Explain.
A
B
D
C
a) Draw the image
of the shape under
a reflection over
the line.
b) Does the final
drawing have
reflectional
symmetry?
Explain.
Go to
SketchPad
Design 1
B’
C’
A’
A
B
D’ D
C
a) Draw the image
of the shape under
a reflection over
the line.
b) Does the final
drawing have
reflectional
symmetry?
Explain.
Go to
SketchPad
Design 2
B
A
D
C
E
a) Draw the image
of the shape under
a reflection over
the line.
A
b) Does the final
drawing have
reflectional
symmetry?
Explain.
Go to
SketchPad
Design 2
B
C’
B’
D
D’
C
E
E’
A’
a) Draw the image
of the shape under
a reflection over
the line.
Go to
SketchPad
Design 3
B
b) Does the final
drawing have
reflectional
symmetry?
Explain.
C
A
E
D
a) Draw the image
of the shape under
a reflection over
the line.
b) Does the final
drawing have
reflectional
symmetry?
Explain.
Go to
SketchPad
Design 3
A’
B
E’
B’
C
A
D
E
D’
C’