Transcript 9.1 Translate Figure and Use Vectors

9.1 Translate Figure and Use
Vectors
Translations
http://www.mathsisfun.com/flash.php?path=%2Fgeometry/images/tr
anslation.swf&w=894&h=762&col=%23FFFFFF&title=Geometry+Tr
anslation
Vector/Translations
http://illuminations.nctm.org/LessonDetail.aspx?id=L474
Rotations
http://illuminations.nctm.org/LessonDetail.aspx?ID=L466#
rotational symmetry
http://illuminations.nctm.org/LessonDetail.aspx?ID=L468
Translation
A translation moves a figure to
a new location.
• same shape
• same size
For all Transformations (including
Translations)
New figure is called an _____________.
image
pre-image
Original figure is called a _____________.
Translate a figure in the coordinate
plane
Example 1:Graph quadrilateral ABCD with
vertices A(-1, 2), B(-1, 5), C(4, 6), and D(4, 3).
Find the image of each vertex after the
translation (x, y) → (x + 3, y – 1). Then graph
the image using prime notation.
Types of Transformations
(Preview- DON’T Write down)
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Translation
Reflection
Rotation
Dilation
are all Isometries
If a transformation is
an Isometry, then the
image is the same
shape and size of it’s
pre-image.
Write a translation rule and verify
congruence
Write a rule for the transformations of ∆ ABC to
∆ A’B’C’. Then verify whether or not each
transformation is an isometry. If so, use a
congruence postulate (SAS, ASA, SSS, AAS).
a)
b)
VECTORS
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A vector is a quantity that has both
direction
_______________
and
magnitude
______________________,
or size.
It is used as another way to describe a
translation
_______________________________.
A vector is represented in the coordinate
plane by an _______________
drawn from
ray
one point to another.
F
G
5,3
Identify vector components
Example 3:
5, -2
Name the vector and write its
component form.
-7, 0
EXAMPLE 4:
The vertices of ∆ABC are A(0, 3), B(2, 4),
and C(1, 0). Translate ∆ABC using the vector
5,-1 .
Example 5: The vertices of ∆ABC are
A(-1, -1), B(0, 2), and C(1, 0). Translate
∆ABC using the vector 5,2 .
Translation Rule
Another way of describing a translation on a
coordinate plane.
For example….
An image of shape translated by the vector
3, -2 would have the same image of a
shape translated by (x,y)  (x+3, y-2).
SUMMARY:
Describing a Translation
There are several ways to indicate that a translation is to occur:
1. Explain the translation from ABCD to
A’B’C’D’ in words.
The pre-image is shifted to the
left 7 units and down 3 units
2. Write the translation rule of ABCD to
A’B’C’D’ in vector form.
3. Write the translation rule for the
translation ABCD to A’B’C’D’.
Lets check!

http://regentsprep.org/regents/math/geometr
y/GT2/PracT.htm
Let’s check your understanding
http://regentsprep.org/regents/math/geometry/
GT2/PracTran.htm