Coordinate
Algebra
Unit 5:
Transformations in the
Coordinate Plane
Excerpts from Georgia Department of
Education Webinar September 20, 2012
melissa.stewart@hallco.org
October 2012
Warm-Up
Seven circles of the same size are
placed in the pattern shown below:
Find as many rigid motions of the
plane as you can which take this
figure onto itself.
Answer:
melissa.stewart@hallco.org
October 2012
What’s the main idea of Unit 5?
• Develop a deep understanding of
definitions of basic geometric figures
(angle, circle, perpendicular line,
parallel line, and line segment)
• Deepen understanding of
transformations in the plane.
melissa.stewart@hallco.org
October 2012
Concepts & Skills to Maintain from Previous Grades
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plotting points on a coordinate plane
congruence of geometric figures and the correspondence of their
vertices, sides, and angles
recognizing line and rotational symmetry
interpreting and sketching views from different perspectives
calculate the perimeter and area of fundamental geometric plane
figures
use the concepts of ratio, proportion, and scale factor to demonstrate
the relationships between similar plane figures
Websites to help with the above:
http://www.crctlessons.com/
www.aaamath.com
http://funbasedlearning.com/algebra/graphing/points/
http://www.superteacherworksheets.com/ordered-pairs.html
melissa.stewart@hallco.org
October 2012
Enduring Understandings from this Unit
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The concepts of congruence, similarity, and symmetry can be
understood from the perspective of geometric transformation.
Fundamental are the rigid motions: translations, rotations, reflections,
and combinations of these, all of which are here assumed to preserve
distance and angles (and therefore shapes in general).
Reflections and rotations each explain a particular type of symmetry,
and the symmetries of an object offer insight into its attributes.
melissa.stewart@hallco.org
October 2012
Examples & Explanations
1.
A Perform the following sequence of
transformations: Rotate counterclockwise 90
degrees about the origin, reflect over the xaxis on ∆TRY with vertices T(-2, 3), R(3, 6),
Y(1, -1).
Perform the first transformation. Graph and state
the coordinates.
T’(-3, -2), R’(-6, 3), Y’(1,1)
Perform the second transformation. Graph and
state the coordinates.
T”(-3, 2), R”(-6, -3), Y”(1, -1)
2.
Perform the following sequence of
transformation, Rotate counterclockwise 90
degrees about the origin, reflect over the xaxis on ∆CAT with vertices
C(X1, Y1), A(X2, Y2), T(X3, Y3).
What are the vertices of the image?
C’(-Y1, -X1), A’(-Y2, -X2), T’(-Y3, -X3)
melissa.stewart@hallco.org
October 2012
3.
Perform the following sequence of
transformation, Rotate counterclockwise 90
degrees about the origin, reflect over the xaxis.
Analyze the coordinates of the pre-image
and the final image. What is the
transformation that is equivalent to the two?
Reflection over y = -x
Additional Resources
Brain Pop Interactive Resources
http://www.brainpop.com/math/geometryandmeasurement/transformation
Geometer’s Sketchpad activities
http://www.keypress.com
The Shodor Educational Foundation
http://www.shodor.org
Math nets Interactive Resource
http://www.mathsnet.net/transform
Escher lesson plans
http://www.ysd.k12.sd.us/lesson%20plans/Johnke_files/The%20World%20o
f%20Escher_files/frame.htm
Escher’s work and Tessellation Activities
http://britton.disted.camosun.bc.ca/jbaraki.htm
NEA Portal Arkansas Video Lessons on-line
http://neaportal.k12.ar.us/index.php/2010/07/points-lines-and-planessegments-rays-and-angles/
Math dictionary
http://www.teachers.ash.org.au/jeather/maths/dictionary.html
Math dictionary at Intermath
http://intermath.coe.uga.edu/dictnary/homepg.asp
National Library of Virtual Manipulatives
http://nlvm.usu.edu/en/nav/frames_asid_298_g_4_t_3.html?open=activities
http://nlvm.usu.edu/en/nav/frames_asid_302_g_4_t_3.html?open=activities
http://nlvm.usu.edu/en/nav/frames_asid_300_g_4_t_3.html?open=activities
melissa.stewart@hallco.org
October 2012
 The student edition for Unit 5 can be
found at
https://www.georgiastandards.org/C
ommon-Core/Pages/Math-9-12.aspx
On the left side, please look under
mathematics, Coordinate Algebra.
Then, the right side has a pull-down
menu to access the units.
 Additional parent guides will be
posted to the parent resource page on
http://www.hallco.org/boe/index.ph
p (right had menu) as they become
available.
melissa.stewart@hallco.org
October 2012