chapter 12. for each example, how would i get the first image to look like the second?
TRANSCRIPT
![Page 1: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/1.jpg)
Chapter 12
![Page 2: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/2.jpg)
For each example, how would I get the first image to look like the second?
![Page 3: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/3.jpg)
What are these examples of?
![Page 4: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/4.jpg)
A transformation of a geometric figure is a change in its position, shape, or size.
Types of transformations: reflection (flip), translation (slide), rotation (turn), dilation (shrink or grow)
Preimage – original figure before the transformation
Image – resulting figure after the transformation
![Page 5: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/5.jpg)
An isometry is a transformation in which the preimage and image are congruent.
In other words, there is a change in position, but not shape or size.
A reflection is an isometry in which the orientation of the object and its image are opposites.
![Page 6: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/6.jpg)
A reflection is an isometry in which the orientation of the object and its image are opposites.
![Page 7: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/7.jpg)
ABCD is an image of KLMN. What is the image of angle L? Which side corresponds to NK?
Sometimes images are named as A’B’C’D’ with the ‘ (prime) signifying the difference between the image and pre-image.
![Page 8: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/8.jpg)
∆XYZ has vertices X(-2,3), Y(1,1), and Z(2,4). Draw ∆XYZ and its reflection image in the x-axis. Name using primes.
![Page 9: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/9.jpg)
∆XYZ has vertices X(-2,3), Y(1,1), and Z(2,4). Draw ∆XYZ and its reflection image in the line x=3. Name using new letters.
![Page 10: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/10.jpg)
A translation is an isometry that maps all points of a figure the same distance in the same direction.
We describe translations using vectors <x,y>
![Page 11: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/11.jpg)
Find the image of F under the translation<-4,1>.
2
1
-1
-2
-2 2 4
J
I
H
G
F
![Page 12: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/12.jpg)
Find the vector that describes the translation H→I.
2
1
-1
-2
-2 2 4
J
I
H
G
F
![Page 13: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/13.jpg)
Find the vector that describes the translation ∆ABC→ ∆A’B’C’.
4
3
2
1
-1
-2
-3
-4
-6 -4 -2 2 4 6
A'
C'
B'
C
B
A
![Page 14: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/14.jpg)
Draw the image of ∆ABC under the translation <5,-2>.
![Page 15: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/15.jpg)
To describe a rotation, you need three pieces of information:1. center of rotation (a point on or off the figure)
ON
Off
![Page 16: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/16.jpg)
2. angle of rotation (positive number, 360 max.)
3. direction of rotation (clockwise or counterclockwise)
![Page 17: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/17.jpg)
Draw the image that results when ABC is rotated counterclockwise 270° around the origin.
![Page 18: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/18.jpg)
A composition of reflections in two parallel lines is a translation. two intersecting lines is a rotation.
A glide reflection is the composition of a glide (translation) and a reflection in a line parallel to the glide vector.
![Page 19: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/19.jpg)
A figure has symmetry if there is an isometry that maps the figure onto itself.
Three types of symmetry: Line symmetry (a.k.a. reflectional
symmetry) Rotational symmetry – is its own image for
some rotation that is less than or equal to 180°
Point symmetry – has rotational symmetry of exactly 180°
![Page 20: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/20.jpg)
What kind of symmetry does each figure have? (could be multiple types)
![Page 21: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/21.jpg)
A tessellation is a repeating pattern of figures that completely covers a plane, without gaps or overlaps.
All triangles and quadrilaterals tessellate.
![Page 22: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/22.jpg)
A regular polygon will tessellate a plane if the interior angle measure will divide into 360 evenly.
![Page 23: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/23.jpg)
![Page 24: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/24.jpg)
A dilation is a transformation whose preimage and image are similar. It is generally not an isometry.
![Page 25: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/25.jpg)
Every dilation has a center and a scale factor. The scale factor describes the size change
from the original figure to the image.
The dilation is an enlargement if the scale factor n > 1.
It is a reduction if the scale factor 0 < n < 1.
![Page 26: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/26.jpg)
![Page 27: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/27.jpg)
The green circle is a dilation of the blue circle. Describe the dilation.
3 cm
8 cm
C
![Page 28: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/28.jpg)
∆ABC is a dilation of ∆DBC. Find the center and scale factor.
2 in.
6 in.
E
A
B
C
D
![Page 29: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/29.jpg)
The scale factor on a museum's floor plan is 1 : 200. The length and width on the drawing are 8 in. and 6 in. Find the actual dimensions in feet and inches.
![Page 30: Chapter 12. For each example, how would I get the first image to look like the second?](https://reader033.vdocuments.net/reader033/viewer/2022051316/5697bfb61a28abf838c9e0fc/html5/thumbnails/30.jpg)
∆XYZ has coordinates X(3,1), Y(2,-4), and Z (-2,0). Find the image for a dilation with center (0,0) and scale factor 2.5.