Lesson Activity: Exploring Reflections
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School
University of South Carolina *
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Course
B221
Subject
Mathematics
Date
Apr 3, 2024
Type
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8
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Lesson Activity: Exploring Reflections
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Lesson Activity
Exploring Reflections
This activity will help you meet this educational goal:
You will represent reflections on the coordinate plane using geometry software.
Directions
Read the instructions for this self-checked activity. Type in your response to each
question, and check your answers. At the end of the activity, write a brief evaluation
of your work.
Activity
Use GeoGebra to predict the results of a reflection . Relaunch the GeoGebra activity
to complete each part. For help, watch this short video about using GeoGebra to
transform figures .
Part A
Reflect quadrilateral across the
x
-axis to produce quadrilateral .
In the table, record the coordinates of the vertices for the image. The coordinates for
the preimage have already been recorded.
Answer:
Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(-3,2)
B
(-2,-1)
B'
(-2,1)
C
(-1,-2)
C'
(-1,2)
D
(-1,-4)
D'
(-1,4)
Space used (includes formatting): 1630 / 15000
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Lesson Activity: Exploring Reflections
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Reflect quadrilateral across the x
-axis to produce quadrilateral .
Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(-3,2)
B
(-2,-1)
B'
(-2,1)
C
(-1,-2)
C'
(-1,2)
D
(-1,-4)
D'
(-1,4)
Hide Sample Answer
Part B
Reflect quadrilateral across the
y
-axis to produce quadrilateral .
In the table, record the coordinates of the vertices for the image. The coordinates for
the preimage have already been recorded.
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Lesson Activity: Exploring Reflections
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Answer:
Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(3,-2)
B
(-2,-1)
B'
(2,-1)
C
(-1,-2)
C'
(1,-2)
D
(-1,-4)
D'
(1,-4)
Space used (includes formatting): 1656 / 15000
Reflect each vertex of quadrilateral across the y
-axis to produce quadrilateral .
Hide Sample Answer
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Lesson Activity: Exploring Reflections
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Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(3,-2)
B
(-2,-1)
B'
(2,-1)
C
(-1,-2)
C'
(1,-2)
D
(-1,-4)
D'
(1,-4)
Part C
Reflect quadrilateral across the line
to produce quadrilateral .
Hint: It may be helpful to first draw the line
, which goes through the origin and .
In the table, record the coordinates of the vertices for the image. The coordinates for
the preimage have already been recorded.
Answer:
Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(-2,-3)
B
(-2,-1)
B'
(-1,-2)
C
(-1,-2)
C'
(-2,-1)
D
(-1,-4)
D'
(-4,-1)
Space used (includes formatting): 1634 / 15000
First draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral .
Hide Sample Answer
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Lesson Activity: Exploring Reflections
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Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(-2,-3)
B
(-2,-1)
B'
(-1,-2)
C
(-1,-2)
C'
(-2,-1)
D
(-1,-4)
D'
(-4,-1)
Part D
Reflect quadrilateral across the line
to produce quadrilateral .
Hint: It may be helpful to first draw the line
, which goes through the origin and
.
In the table, record the coordinates of the vertices for the image. The coordinates for
the preimage have already been recorded.
2/1/24, 11
:
11 PM
Lesson Activity: Exploring Reflections
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Answer:
Vertex
Preimage Coordinates
Vertex
Image Coordinates
A
(-3,-2)
A'
(2,3)
B
(-2,-1)
B'
(1,2)
C
(-1,-2)
C'
(2,1)
D
(-1,-4)
D'
(4,1)
Space used (includes formatting): 1600 / 15000
First draw the line on the graph. Then reflect each vertex of quadrilateral across the line to produce quadrilateral .
Vertex
Preimage Coordinates
Vertex
Image Coordinates
Hide Sample Answer
Your preview ends here
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Lesson Activity: Exploring Reflections
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A
(-3,-2)
A'
(2,3)
B
(-2,-1)
B'
(1,2)
C
(-1,-2)
C'
(2,1)
D
(-1,-4)
D'
(4,1)
Part E
Analyze each table of coordinates that you completed. What patterns do you see in
how the coordinates changed?
Answer:
All of the y-coordinates in section A went from negative to positive, but all of the x-coordinates
remained same. Part B shows that while all of the x-coordinates shifted from negative to positive,
the y-coordinates remained unchanged. In section C, the x- and y-coordinates were inverted. The
x- and y-coordinates were rearranged in section D, and all coordinates went from negative to
positive.
Space used (includes formatting): 403 / 15000
In part A, all of the
x
-coordinates stayed the same, but all of the y
-coordinates
changed from negative to positive. In part B, all of the y
-coordinates stayed the same,
but all of the x
-coordinates changed from negative to positive. In part C, the order of
the
x
- and y
-coordinates switched. In part D, the order of the
x
- and y
-coordinates
switched, and all coordinates changed from negative to positive.
Hide Sample Answer
Self-Evaluation
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How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then
write a brief evaluation of your work below. Note what you learned and what
challenged you.
Answer:
3-5 i think i couldve done a little better and i think i am definitly understanding its jsut writting it
out
Space used (includes formatting): 135 / 15000