Transcript http://iblog.dearbornschools.org/dhsgeometry/wp-content/uploads/sites/421/2013/09/GEOMETRY-UNIT-1.ppt

GEOMETRY UNIT 1
Transformations
1
Types of Transformations
Reflections: These are like mirror images as seen across a line or
a point.
Translations ( or slides): This moves the figure to a new location
with no change to the looks of the figure.
Rotations: This turns the figure clockwise or
counter-clockwise but doesn’t change the
figure.
Dilations: This reduces or enlarges the figure to a
similar figure.
2
The Vocabulary of Transformation Geometry
• The original figure is called the preimage; the new (copied) picture is called
the image of the transformation.
• A rigid transformation is one in which
the pre-image and the image both have
the exact same size and shape.
• In short, a transformation is a
copy of a geometric figure, where
the copy holds certain
properties. Think of when you
copy/paste a picture on your
computer.
• A rigid transformation is one in
which the pre-image and the
image both have the exact
same size and shape.
Translations - Each Point is Moved the Same Way
• The most basic transformation is the
translation. The formal definition of
a translation is "every point of the
pre-image is moved the same
distance in the same direction to
form the image."
• Each translation follows a rule. In
this case, the rule is "5 to the right
and 3 up." You can also translate
a pre-image to the left, down, or
any combination of two of the
four directions.
Translation
(x, y)
(x + 5, y + 0)
y
A’
A
B’
B
C
C’
x
Pre-image
Image
A (-2, 4)
A’ (3, 4)
B (-3, 2)
B’ (2, 2)
C (-1, 1)
C’ (4, 1)
Translation
(x, y)
(x + 0, y - 5)
y
A
B
C
x
A’
Pre-image
A (-2, 4)
Image
B’
C’
A’ (-2, -1)
B (-3, 2)
B’ (-3, -3)
C (-1, 1)
C’ (-1, -4)
Translation
(x, y)
(x + 3, y - 4)
y
A
B
C
A’
x
B’
Pre-image
C’
Image
A (-2, 4)
A’ (1, 0)
B (-3, 2)
B’ (0, -2)
C (-1, 1)
C’ (2, -3)
Click on link below to watch youtube video of transformations. ONLY watch the first 2
minutes!!!!!
http://www.youtube.com/watch?feature=player_detailpage&v=geu016oz
m_8
Which of the figures below is the pre-image? Which is the
image? What is the difference? How can you recognize
which is which????
What is the RULE for the translation to
the left?
A’ (1,4)
D’ (1,1)
B’ (7,4)
C’ (7,1)
A (-2,-1)
B (4,-1)
D (-2,-4)
C (4,-4)
(x,y)
? , y + ____
? )
(x + ____
What is the RULE for the translation above?
(write rule on chalkboard)
• You will now be given a sheet of large graph paper. Everyone at your
table MUST work together to complete this assignment.
• Write the first and last names of everyone at your table on the back of
the grid paper IN PENCIL!!!!
• Create a large coordinate plane on your graph paper with the origin (0,0)
near the center of the paper. You will end up with four quadrants and
both positive and negative numbers. Write numbers on both the x-axis
and y-axis. Your finished product should look similar to the graph below:
• Draw a red triangle using the coordinates A =(5,5) B=(7,5) C=(7, 10)
• Translate the red triangle using the rule (x,y) (x + 3, y + 4). Draw the new
triangle in black and label the vertices A’, B’, C’.
• Draw a blue quadrilateral.
D=(-1,0) E=(-1,3) F=(-4,3) G=(-4,0)
• Translate the blue quadrilateral using the rule (x,y) (x + 0, y - 7). Draw
your new shape in black and label the new points with D’, E’, F’, G’.
• Draw an irregular pentagon in orange. M=(8,-7) N=(11,-9) O=(9,-11)
P=(8,-9) Q=(5,-9)
• Translate the concave orange pentagon into quadrant II. Be sure to keep it
the EXACT same size and shape. Label your new points “prime” and write
the rule you followed on the graph next to your shape.
• Draw one more polygon shape in purple, translate it, and write your rule
next to the translation.
• When your group has finished this poster, raise your hands and have a
teacher check your work before getting your homework assignment.