Presentation is loading. Please wait.

Presentation is loading. Please wait.

FeatureLesson Geometry Lesson Main Tell what type(s) of symmetry each figure has. 1.D 2.O reflectional: horizontal line of symmetry reflectional: horizontal.

Similar presentations


Presentation on theme: "FeatureLesson Geometry Lesson Main Tell what type(s) of symmetry each figure has. 1.D 2.O reflectional: horizontal line of symmetry reflectional: horizontal."— Presentation transcript:

1 FeatureLesson Geometry Lesson Main Tell what type(s) of symmetry each figure has. 1.D 2.O reflectional: horizontal line of symmetry reflectional: horizontal and vertical lines of symmetry; rotational: point symmetry Draw each figure and all its lines of symmetry. 3. isosceles right triangle4.rhombus that is not a square Lesson 9-4 Symmetry 5.The star below appears on the United States flag. If the star has line symmetry, sketch it and draw the line(s) of symmetry. If it has rotational symmetry, state the angle of rotation. 72° rotational symmetry Lesson Quiz 9-5

2 FeatureLesson Geometry Lesson Main

3 FeatureLesson Geometry Lesson Main

4 FeatureLesson Geometry Lesson Main Lesson 9-5 Dilations 9-5 A dilation is a transformation that changes the size of a figure but not the shape. The image and the preimage of a figure under a dilation are similar.

5 FeatureLesson Geometry Lesson Main Lesson 9-5 Dilations 9-5

6 FeatureLesson Geometry Lesson Main Lesson 9-5 Dilations 9-5

7 FeatureLesson Geometry Lesson Main Lesson 9-5 Dilations 9-5 For a dilation with scale factor n, if n > 0, the figure is not turned or flipped. If n < 0, the figure is rotated by 180°. Helpful Hint

8 FeatureLesson Geometry Lesson Main Lesson 9-5 Dilations 9-5 If the scale factor of a dilation is negative, the preimage is rotated by 180°. For k > 0, a dilation with a scale factor of –k is equivalent to the composition of a dilation with a scale factor of k that is rotated 180° about the center of dilation.

9 FeatureLesson Geometry Lesson Main Circle A with 3-cm diameter and center C is a dilation of concentric circle B with 8-cm diameter. Describe the dilation. The circles are concentric, so the dilation has center C. Because the diameter of the dilation image is smaller, the dilation is a reduction. The dilation is a reduction with center C and scale factor Lesson 9-5 Dilations scale factor: diameter of dilation image diameter of preimage 3838 = Quick Check Additional Examples 9-5 Finding a Scale Factor

10 FeatureLesson Geometry Lesson Main The scale factor on a museums 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. Multiply each dimension on the drawing by 200 to find the actual dimensions. Then write the dimensions in feet and inches. 8 in. X 200 = 1600 in. = 133 ft, 4 in. 6 in. X 200 = 1200 in. = 100 ft The museum floor measures 133 ft, 4 in. by 100 ft. Lesson 9-5 Dilations The floor plan is a reduction of the actual dimensions by a scale factor of Quick Check Additional Examples 9-5 Real-World Connection

11 FeatureLesson Geometry Lesson Main ABC has vertices A(–2, –3), B(0, 4), and C(6, –12). What are the coordinates of the image of ABC for a dilation with center (0, 0) and scale factor 0.75? Lesson 9-5 Dilations The scale factor is 0.75, so use the rule (x, y) (0.75x, 0.75y). A' is (0.75(–2), 0.75(–3)). B' is (0.75(0), 0.75(4)). C' is (0.75(6), 0.75(–12)). The vertices of the reduction image of ABC are A' (–1.5, –2.25), B' (0, 3), and C' (4.5, –9). Quick Check Additional Examples 9-5 Graphing Dilation Images

12 FeatureLesson Geometry Lesson Main 1.A model is a reduction of a real tractor by the scale factor of 1 : 16. Its dimensions are 1.2 ft by 0.6 ft by ft. Find the actual dimensions of the tractor ft by 9.6 ft by 10 ft For Exercises 2 and 3, XYZ has vertices X(3, 1), Y(2, –4), and Z(–2, 0). 2.Use scalar multiplication to find the image of XYZ for a dilation with center (0, 0) and scale factor 2.5. X (7.5, 2.5), Y (5, –10), Z (–5, 0) Lesson 9-5 Dilations 3.Draw and label the preimage and image. For Exercises 4 and 5, DIL is a dilation image of DAT. 4.Identify the center of dilation. 5.Find the scale factor. D 4 Lesson Quiz 9-5

13 FeatureLesson Geometry Lesson Main Determine the scale drawing dimensions of a room using a scale of in. = 1 ft. 1.kitchen: 12 ft by 16 ft 2.bedroom: 8 ft by 10 ft 3.laundry room: 6 ft by 9 ft4.bathroom: 5 ft by 7 ft 1414 (For help, go to Lesson 7-1.) Lesson 9-5 Dilations Check Skills Youll Need 9-5

14 FeatureLesson Geometry Lesson Main Solutions Lesson 9-5 Dilations 1. in. = 1 ft 12 in. = in. = 12 ft; in. = 1 ft 16 in. = 16 1 ft 4 in. = 16 ft. The dimensions of the scale drawing are 3 in. by 4 in in. = 1 ft 8 in. = in. = 8 ft; in. = 1 ft 10 in. = 10 1 ft 2.5 in. = 10 ft. The dimensions of the scale drawing are 2 in. by 2.5 in in. = 1 ft 6 in. = in. = 6 ft; in. = 1 ft 9 in. = 9 1 ft 2.25 in. = 9 ft. The dimensions of the scale drawing are 1.5 in. by 2.25 in in. = 1 ft 5 in. = in. = 5 ft; in. = 1 ft 7 in. = 7 1 ft 1.75 in. = 9 ft. The dimensions of the scale drawing are 1.25 in. by 1.75 in Check Skills Youll Need 9-5


Download ppt "FeatureLesson Geometry Lesson Main Tell what type(s) of symmetry each figure has. 1.D 2.O reflectional: horizontal line of symmetry reflectional: horizontal."

Similar presentations


Ads by Google