Transcript 9.1 Reflections 9.2 Translations

Advanced Geometry
Rigid Transformations
Lesson 1
Translations
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
Terminology
Pre-image
Definition – a figure that undergoes a
motion or transformation
Image
Definition – a figure that results from a
transformation of a figure
Translation
Slide all points of a figure
distance in the same __________.
direction
the same __________
Rectangle ABCD was
translated 5 units right
and 2 units up.
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)
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.
Example:
Find the translation that moves each figure on the
coordinate plane. Write the translation as a sentence
and in coordinate form.
Example:
Triangle TUV is translated 3 units up and 5 units left
to create ∆T’U’V’ with vertices T’(-6, -1), U’(1, 5), and
V’(0, -2). What are the coordinates of the vertices
of ∆TUV?
Terminology
Translations are congruence transformations,
or isometries.
They preserve:
• distance (length of segments)
• angle measures
• betweenness of points
• collinearity
Discussion
Triangle ABC is translated to ∆DEF .
Compare and contrast the figures.
A transformation made up of successive
composition
transformations is called a _______________.
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.
Using a Protractor