Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
Name: ______________________________ Period: __________ Date: ___________
Scale Factor =
∆ABC has been enlarged by a scale factor of 3. What are the coordinates of its image? A (1,1) A’( , ) B (1,3) B’( , ) C (3,1) C’( , )
Dilations
Dilations
Dilations
“Enlarges” or “Reduces” a figure using a scale factor.
A
B
C 2
2
A’ side length
B’
C’
6
6
1. What is the relationship between the new coordinates and the scale factor?
2. If ∆ABC is dilated by a scale factor of 4, what
are the coordinates of ∆A’B’C’? 3. If ∆ABC is dilated by a scale factor of 1/3, what
are the coordinates of ∆A’B’C’?
A dilation with a scale factor greater than 1
is called an _______________.
The image is _________________ than the
original.
A dilation with a scale factor less than 1 is
called a ___________________.
The image is ____________________ than
the original.
B
C
A’
B’
C’
A
Practice: 1. A rectangle is dilated with a scale factor of 0.6. Is the image a reduction or an enlargement? 2. 3. Find the coordinates of the image of quadrilateral KLMN after a dilation with a scale factor of 3/2.
4. You are reducing a digital photo that is 2 in. high and 3 in. wide. If the reduced photo is
in. high, what is
its width? 5. Find the coordinates of the image of quadrilateral RSTU after a dilation with the given scale factor. Graph
the image.
a. scale factor: 2 b. scale factor
a. Figure A has been dilated to figure A’. What is its scale factor?
b. Figure B has been dilated to figure B’. What is its scale factor?
R U
T S
K N
M L
A
A’
B B’
K( , ) _K’_________________ L( , ) _L’_________________ M( , ) _M’_________________ N( , ) _N’_________________
R( , ) ________________ _______________
S( , ) ________________ _______________
T( , ) ________________ _______________
U( , ) ________________ _______________
WHAT EFFECT DOES SCALE FACTOR HAVE ON PERIMETER? 6. ∆A’B’C’ is the image of ∆ABC after a dilation.
7. List the dimensions, the area, and perimeter of rectangle HIJK?
Dimensions: _____________________________
Area: _____________ Perimeter: _____________ 8. Dilate the image by 0.5.
Dimensions: _____________________________
Area: _____________ Perimeter: _____________ 9. Write the ratio of the dilated perimeter to the original perimeter. Do the same for the areas.
10. Multiply the original perimeter by the scale factor. 11. Multiply the original area by (scale factor)2.
Scale Factor
Perimeter of Original Figure
Perimeter of the Dilation
SF SF2 Area of
Original Figure Area of
the Dilation
1 10
RSTU (2 by 3)
1 1 6
RSTU (2 by 3)
2 10
R’S’T’U’ (4 by 6)
2 4 6
R’S’T’U’ (4 by 6)
3 10
R’’S’’T’’U’’ (6 by 9)
3 9 6
R’’S’’T’’U’’ (6 by 9)
4 10
R’’’S’’’T’’’U’’’ (8 by 12)
4 16 6
R’’’S’’’T’’’U’’’ (8 by 12)
What is the result when the original perimeter is multiplied by the scale factor used to dilate the figure?
What is the result if the original area is multiplied by the scale factor squared?
A
B
C 10 cm
7 cm
A’
B’
C’
24 cm 28 cm
What is the ratio of the perimeter of ∆A’B’C’ to the perimeter of ∆ABC?
R U
T S
2
3
J
K
I
H
SCALE FACTOR and ITS EFFECT ON PERIMETER and AREA.
Name: ________________________ Period: ____________ Date: ___________
Mixed Practice Homework
Translations, Reflections, Rotations, Dilations, Similar Figures, Scale Factor 1. Determine if the following polygons are similar.
a. b.
2. ∆ABC is similar to ∆EFG. Find the value of x.
Then find the scale factor if ∆ABC is dilated to form ∆EFG?
3. Quadrilateral WXYZ is similar to quadrilateral LMNP.
Find the values of x and y.
4. Graph the polygon with the given vertices. Dilate by the scale factor K and graph the image.
L(−2, −2), M(−2, −6), N(−6,−10) , Q(−6,0); k =
5. You are making a large gingerbread house that is
similar in shape to a real house. The real house is 25 feet tall and 40 feet wide. The gingerbread house is 2.5 feet tall. How wide should you make the gingerbread house?
6. Use the graph to tell what type of transformation is
shown. A. translation B. reflection over the x-axis C. reflection over the y-axis D. 90° clockwise rotation
Use the graph below for questions 7 and 8. 7. Circle N passes through points (1,1), (5,5), (9,1), and
(5,-3). If you slide the circle 2 units up and 2 units to the left, what will be the new coordinates of the center of circle N?
A (5,3) B (4,2) C (3,3) D (3,2) 8. If you slide triangle DEF 2 units down and 1 unit to
the right, what will be the new coordinates of vertex F?
A (1,1) B (1,5) C (2,1) D (2,2) 9. Margie wants to slide the triangle so that the
coordinates for vertex P are (6,1). Write a rule that tells how Margie should slide the triangle.
10. If trapezoid ABCD is reflected across the y-axis, what will be the new coordinates of the vertices? Graph the image.
AA” A 11. Cheryl drew triangle KLM as shown on the graph
below.
She began to draw a translation of triangle KLM as shown on the graph below. What should the coordinates for vertex K’ be?
A’= _________ B’ = _________ C’ = _________ D’ = _________
12. If triangle RST is reflected across the y-axis, what will be the new coordinates of its image?
13. Which of the following appears to be a reflection
over ̅̅ ̅ ?
14. Describe the transformation below. 15. EFGH is the image of ABCD after dilation. The
vertices of ABCD and EFGH are listed below A (-1,2) E(-4,8)
B (3,2) F(12,8) Graph the figures below.
C (3,-1) G(12,-4)
D(-1,-1) H (-4,-4) a. What is the scale factor? b. What is the perimeter of ABCD?
c. How is the ratio of the perimeter of EFGH to the perimeter of ABCD related to the scale factor?
d. What is the area of ABCD?
e. How is the ratio of the area of EFGH to the area of ABCD related to the scale factor?
R’= _________ S’ = _________ T’ = _________
16. The vertices of triangle JLK are listed below. J(-4,-3) K(-2,0) L(1,2)
Kim rotated the triangle 90° clockwise. Describe and correct the error Kim made when finding the coordinates of the vertices of the rotated image.
17. Graph ∆LMN with vertices L(2,0), M(2,3), and
N(6,0). Then graph its image after the following transformations.
a. Rotate 180°. b. Translate using (x, y) (x – 3, y – 4)
18. Graph ∆LMN with vertices L(2,0), M(2,3), and N(6,0). Then graph its image after the following transformations.
a. Rotate 90° counterclockwise. b. Reflect over the y-axis.
Kim’s Work
(x,y) (-y,x) J(-4,-3) J’ (3,-4) K(-2,0) K’(0,-2)
L(1,2) L’(-2,1) The vertices are: (3,-4), (0,-2), and (-2,1)