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Name:________________________________________ Date:______ Period:_____
Name:________________________________________
Geometry
Date:______
Period:_____
Translations on the Coordinate Plane: Notes
Do Now:
1.) Describe, in words, 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?
Vocabulary:
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)
Examining the Translation
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.
3.) Given ∆LOU with L(-4, -4), O(-2, -1), and U(-6, -3).
(a) Graph ∆LOU on the axes provided.
(b) On the same set of axes, graph ∆L'O'U',
the image of ∆LOU after T3,-5.
(c) On the same set of axes, graph ∆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:________________________________________
Geometry
Date:______
Period:_____
Translations on the Coordinate Plane: Homework
1.) The graph below shows
(a) Graph and label
, the image of
, the pre-image of
(b) Graph and label
, the image of
after a
. 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
of
after a T4, 5.
(c)Graph and state the coordinates of
of
after a T-10,-8.
(d) State one translation that would map
.
after it was reflected over the y-axis.
.
,
the image
, the image
onto
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.) Copy the given angle using segment BC.
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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