Advanced Geometry

1

• Advanced Geometry
• Rigid Transformations
• Lesson 1

Translations
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Terminology
Transformation
Definition - the movement of a figure in a plane
from its original position to a new position
Rigid transformation
does not change the size or shape of the figure
congruence transformation
isometry
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Terminology
Pre-image
Definition a figure that undergoes a motion or
transformation
Image
Definition a figure that results from a
transformation of a figure
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Translation
Slide
all points of a figure the same __________ in
the same __________.
distance
direction
Rectangle ABCD was translated 5 units right and 2
units up.
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Notation
Coordinate Form
Rectangle ABCD was translated 5 units right and 2
units up.
5 units right
x 5
2 units up
y 2
(x, y)
?
(x 5,
y 2)
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Example Quadrilateral HJLK has vertices H(-1,
0), J(0, 2), L(3, 1), and K(2, -2) is
translated by (x, y) ? (x 3, y 3).
Graph HJLK and its image. List the coordinates
of the image.
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Example Find the translation that moves each
figure on the coordinate plane. Write the
translation as a sentence and in coordinate
form.
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Example Triangle TUV is translated 3 units up
and 5 units left to create ?TUV
with vertices T(-6, -1), U(1, 5), and
V(0, -2). What are the coordinates of the
vertices of ?TUV?
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Terminology
Translations are congruence transformations, or
isometries.
They preserve

• distance (length of segments)

• angle measures

• betweenness of points

• collinearity

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Discussion
Triangle ABC is translated to ?DEF . Compare
and contrast the figures.
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A transformation made up of successive
transformations is called a _______________.
composition
Example Rectangle MNPQ with vertices M(-3,
-1), N(1, -1), P(1, 4), and Q(-3, 4) is
translated down 4 and right 6 units. That
image is then translated up 3 and left 7 units.
Write the coordinate form of each translation
and then the composition.
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Using a Protractor