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Document 1279921
Name: _____________________________________________________________
Date: ______________________
Period: ______
Chapter 4: Transformations
Topic 3: Translations ON the Coordinate Plane
Do Now:
1.) Describe, in direction and numbers, how to get from ∆ABC to its image ∆A'B'C'.
2.) Is the size of the object preserved?
3.) Is the order of the vertices the same?
4.) What type of isometry is occurring here?
Translations:
Another type of __________________________________ is called a _________________________. A _________________________ is
considered to be a "slide". When a _____________________ is performed, every point of a figure is moved
the same distance in the same direction.
A ____________________________ is considered to be __________________ isometry because it preserves size and order of
all of the vertices.
Notation:
Ta,b(x,y)  _________________
or you may see it as
(x, y)  (x + a, y + b)
Where  represents the movement along the x-axis, and  represents the movement along the y-axis
Name: _____________________________________________________________
Examining the Translation
Date: ______________________
Period: ______
Using the same translation as the Do Now we are going to explore
the path that the image follows.
Using rays (), connect the pre-image with the image points.
What do you notice about all of the rays that you have drawn?
__________________________________________________________
_____________________________________________________
This ray is called a ____________________.
A ____________________ is a directed line segment that has both length and direction.
Examples:
1.) Draw the vector that defines each translation below.
2.) Using the diagram, translate the figure one unit down and three units to the right. Write each new
coordinate. Draw the vector that defines the translation.
Name: _____________________________________________________________
3.) Given ∆LOU with L(-4, -4), O(-2, -1), and U(-6, -3).
(a) Graph ∆LOU on the axes provided.
Date: ______________________
Period: ______
(b) On the same set of axes, graph and state ∆L'O'U',
the image of ∆LOU after T3,-5.
(c) On the same set of axes, graph and state ∆L"O"U",
the image of ∆L'O'U' after a T5,6.
(d) Name a single translation that will map ∆LOU
onto ∆L"O"U".
4.) Determine the coordinates of the image of point (6, -5) under T-7,3.
5.) Determine the coordinates of the image of point (-8, -3) under the translation (x, y) ---> (x + 4, y - 7).
6.) Determine the translation that maps the point (-5, 5) to the point (7, 1).
7.) A translation maps the point (-2, 5) to the point (-4, -4). What is the image of (1, 4) under that same
translation?
Name: _____________________________________________________________
Date: ______________________
Topic 3 Homework: Translations ON the Coordinate Plane
1.) The graph below shows ∆′′′, the image of ∆ after it was reflected over the y-axis.
(a) Graph and state ∆, the pre-image of ∆′′′.
(b) Graph and state ∆′′′′′′, the image of ∆′′′,
after a −2,−5. State the coordinates below.
2.) Given ∆ with D(1,1), O(3,5), and G(5,2).
(a) Graph and label ∆.
(b) Graph and state the coordinates of ∆ ′ ′  ′ , the image
of ∆ after a T4, 5.
(c)Graph and state the coordinates of ∆""", the image
of ∆′′′ after a T-10,-8.
(d) State one translation that would map ∆ onto
∆""".
Period: ______
Name: _____________________________________________________________
Date: ______________________
Period: ______
3.) A translation maps point A(5, -1) to point A’(6, 2). What is the image of B(8, 7) under that same
translation?
4.) A translation maps point (-3, -5) onto point (-5, -2). What is the image of point (6, 4) under that same
translation?
Review Questions:
̅̅̅̅ .
5.) Create a line parallel to 
6.) The solution of the system of equations y = x2 – 2 and y = x is
(1) (1, 1) and (-2, -2)
(3) (1, 1) and (2, 2)
(2) (2, 2) and (-1, -1)
(4) (-2, -2) and (-1, -1)
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