I can draw glide reflections and other compositions of isometries in the coordinate plane If the images to the right describe a composition of transformations in your own words define composition of transformations ID: 532443
Download Presentation The PPT/PDF document "9.4 : Compositions of Transformations" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
9.4 : Compositions of Transformations
I can draw glide reflections and other compositions of isometries in the coordinate plane.Slide2
If the images to the right describe a composition of transformations, in your own words, define composition of transformations: Slide3
Vocabulary!
Composition of Transformations
Glide Reflection
a transformation is applied to a preimage and then a 2nd transformation is applied to the image.*2nd image is double prime (“)
The composition of a translation followed by a reflectionin a line parallel to the translation vector.Slide4
Example 1:
Quadrilateral
BGTS
has vertices
B
(–3, 4),
G(–1, 3), T(–1 , 1), and S(–4, 2). Graph BGTS and its image after a translation along 5, 0 and a reflection in the x-axis.Slide5
Vocabulary!
Isometry
A transformation that keeps the image the
same size and shape as the
preimage
Composition of Isometries(Transformations) The composition of two or more isometries is an isometry.
Example: the composition of a reflection and then a rotation is an isometry because neither transformation changes size or shape of figureSlide6
Example 2:
Δ
TUV
has vertices
T
(2, –1),
U(5, –2), and V(3, –4). Graph ΔTUV and its image after a translation along –1 , 5 and a rotation 180° about the origin.Slide7
Example 3:
If PQRS is translated along
and reflected in
about the origin, what are the coordinates of P’’Q’’R’’S’’? If P(3,2), Q(4,1), R(-1,2) and S(3,4).
Slide8
Example 4:
Quadrilateral ABCD with A(1, 5), B(6, 2), C(-1, 3), D(-4, -2) is reflected in the line y = x and then rotated 90°. Find the coordinates of the image.Slide9
Vocabulary!
Reflections in Parallel Lines
Reflections in Intersecting Lines
The composition of two reflections in parallel
lines
can be described by a translation vector that is
perpendicular to the two lines and twice the
distance between the two lines.
The
composition of two reflections in
intersecting
lines
is the same as a
rotation about the point
where the lines intersect and through an angle
that is twice the measure of the acute or right
angle formed by the lines.Slide10
Example 6:
A triangle is reflected in two parallel lines. The composition of the reflection produces a translation 22 centimeters to the right. How far apart are the parallel lines?