Warm-up. Translations Using arrow notation to write a rule. Example: 1) Write a rule that would move a point 3 units to the right and 5 units down.
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1 Translations Using arrow notation to write a rule. Example: 1) Write a rule that would move a point 3 units to the right and 5 units down. (x, y) 2) Write a rule that would move a point 6 units down. (x, y) 3) Write a rule that would move a point 8 units to the left. (x, y) Warm-up Reflections Give the coordinates of the image of each point after a reflection in axis indicated. 4) (5, 7) ; x axis 5) (3, 4) ; y axis 6) ( 8, 2) ; x axis 7) ( 5, 1) ; y axis
2 Dilations Dilation is a type of transformation that causes an image to stretch or shrink in proportion to its original size.
3 A Dilation is a transformation that changes the size, but not the shape, of a figure. Think about how your pupils dilate when you have to go to the eye doctor. What Changes??? Dilation
4 ENLARGEMENT small BIG is when you multiply by a scale factor > 1 reduction is when you multiply by a scale factor < 1 (a fraction) BIG small 1:1 Scale Factor A Scale factor of 1 does not affect the size of the figure
5 Scale Factor the number you multiply by Rule for a dilation with a scale factor of n (x, y) (nx, ny) Multiply BOTH coordinates by the given Scale Factor. To find the scale factor of a figure, choose a pair of corresponding sides and use the ratio: Scale Factor Formula Just say "NO" NEW ORIGINAL
6 Let's Practice Give the coordinates of the image of triangle ABC with vertices A(6, 6), B(6, 3), and C(9, 3) after a dilation of: 1) Scale factor of 2 with the origin as the center of dilation. 2) Scale factor of 1/3 with the origin as the center of dilation. Solution A A B C A'' A' B' C' B'' C'' B''' C'''
7 Similar Figures Because a scale factor is used, dilations create figures which are similar. Similar figures: have the same shape but not necessarily the same size. Their corresponding angles are congruent Their corresponding sides are proportional in length (that means they have the same ratio or scale factor)
8 Identify the scale factor in the pairs of images shown below give the length of the sides. Image 1 8 A' C' Image 2 C 6 10 A B' B 4 A C 3 5 B 2 2 C' A' 1 B' 6 Are the two figures similar? Why or Why not?
9 Activity Press the pair of images that has a dilated image in it
10 Activity Identify Scale Factor (1st determine if it is > 1 or < 1) Scale factor = 2 Scale Factor > 1 Scale factor = 1/4 Scale Factor > 0 and < 1 Scale factor = 3 Scale Factor > 1 Scale factor = 1/3 Scale Factor > 0 and < 1 C Scale factor = 2 Scale Factor > 1 Scale factor = ½ Scale Factor > 0 and < 1 Scale factor = 3 Scale Factor > 1 Scale factor = 1/6 Scale Factor > 0 and < 1
11 Teacher's Notes Identify the pair that has the dilated image in it.
12 Constructing Dilations Create the dilated image of a square, whose side measures 2 cm, with the origin as the center of dilation, and a scale factor of 2. original coordinates A B C D Solution C D dilated coordinates A' B' C' D' 1 A B 1 o
13 Constructing Dilations Dilate square ABCD with the origin as the center of dilation and a scale factor of 1/3 C original coordinates A B C D Solution C ' A ' D B ' ' C A D B dilated coordinates A' B' C' D'
14 Constructing Dilations Dilate square ABCD with the origin as the center of dilation and a scale factor of 4. C original coordinates A B C D Solution 8 8 C' D' C C D D A B A B dilated coordinates A' B' C' D' 7 7 A' B' 8 8
15 Constructing Dilations Draw a dilation of a right angled triangle with sides, 2 cm, 2 cm, and 2.82 cm, with the scale factor of 2 using the origin as the center of dilation. original coordinates A B C Dilated Image C A B dilated coordinates A' B' C' 1 1 0O
16 Check Your Understanding 1 Dilation is a type of transformation that causes an image to stretch or shrink in proportion to its original size. True False Select the correct answer.
17 Check Your Understanding 2 The ratio by which the image stretches or shrinks is known as the scale factor. True False Select the correct answer.
18 Check Your Understanding 3 Dilations create similar images with the change in the length of the sides or the area. True False Select the correct answer.
19 Check Your Understanding 4 Rectangle A' B' C' D' is a dilated image of rectangle ABCD. True 8 False A B A' B' D D' C' C Select the correct answer.
20 Check Your Understanding 5 A table is 6 cm wide. After dilation, the table is 3 cm wide. Calculate the scale factor for this dilation. A 1 B 2 C 1/2 D 1/3 Select the correct answer.
21 Check Your Understanding 6 If a balloon of diameter 2 cm is dilated with a scale factor of 1.5, then what is the diameter of the dilated balloon? A 3 B 4 C 5 D 6 Select the correct answer.
22 Check Your Understanding 7 What is the scale factor for the given pair of images? A 2 48 inches B ½ 12 inches C 4 D ¼ Select the correct answer.
23 Check Your Understanding 8 Identify the value of 'a' in the graphic. A 1 B 2 C 3 D 4 Select the correct answer.
24 Check Your Understanding 9 What is the scale factor of the dilation with centre as the origin? A 2 B ½ C 2 D 1/2 Select the correct answer.
25 Check Your Understanding 10 What is the scale factor when triangle A (0,2), B ( 2,2), C( 2,0) is dilated to A'(0,8), B'( 8,8), C'( 8,0)? A 2 B 2.5 C 4 D 4.5 Select the correct answer.
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Vocabulary. Term Page Definition Clarifying Example. center of dilation. composition of transformations. enlargement. glide reflection.
CHAPTER 12 Vocabulary The table contains important vocabulary terms from Chapter 12. As you work through the chapter, fill in the page number, definition, and a clarifying example. center of dilation Term
Name: 1) Which of the following properties of an object are not preserved under a rotation? A) orientation B) none of these C) shape D) size
Name: 1) Which of the following properties of an object are not preserved under a rotation? A) orientation B) none of these C) shape D) size 2) Under a certain transformation, A B C is the image of ABC.
UNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 1: Exploring Trigonometric Ratios Instruction
Prerequisite Skills This lesson requires the use of the following skills: measuring angles with a protractor understanding how to label angles and sides in triangles converting fractions into decimals
Methods in Mathematics
Write your name here Surname Other names Pearson Edexcel GCSE Centre Number Candidate Number Methods in Mathematics Unit 2: Methods 2 For Approved Pilot Centres ONLY Foundation Tier Wednesday 12 November
Exterior Only this column when the polygon is 1) a) Find the value of x. c) Find the value of x. b) Find the value of x. d) Find the value of x.
Not a question, write this on the top of your Test Corrections underneath the heading. Sum Each Angle Interior Exterior Only this column when the polygon is 1) a) Find the value of x. c) Find the value
Measuring Triangles. 1 cm 2. 1 cm. 1 cm
3 Measuring Triangles You can find the area of a figure by drawing it on a grid (or covering it with a transparent grid) and counting squares, but this can be very time consuming. In Investigation 1, you