University:
High School
Course:
High School Mathematics
Academic year:

2024
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294

Pages:

3
Author:

KLogan

Chapter 4 Study Guide: Geometry 4.1 Translations "Sliding" or "moving" the figure Right or left Up or down Graph ΔABC with vertices A(1,2), B(3,-1), and C(0,1) and its image after the translation. (x,y) → (x-5,y-3) (x,y) → (x,y+2) Graph ΔABC and its image after the composition. Translation: (x,y) → (x+4,y+1) Translation: (x,y) → (x+2,y-5) 4.2 Reflections "Flips" or "mirrors" the figure Rules for (a,b) x-axis: (a,-b) y-axis: (-a,b) y = x: (b,a) y = -x: (-b,-a) Lines of Symmetry divides object into two identical parts Graph ΔABC with vertices A(1,2), B(3,-1), and C(0,1) and its image after the reflection in the given line. x-axis y-axis x = 2 How many lines of symmetry does the figure have? 2 5 none Image Analysis Visual Elements: Text: The primary content of the image consists of handwritten text, including the title "Chapter 4 Study Guide: Geometry," section headings, definitions, instructions, and mathematical expressions. Diagrams: There are multiple diagrams illustrating triangles, coordinate planes, and transformations. Arrows: Arrows are used to indicate the direction of translations and reflections. Textual Content: Chapter 4 Study Guide: Geometry 4.5 Dilations Changing the shape of the object by the scale factor k k > 1 on enlargement k < 1 is a reduction (shrink) Graph the triangle and its image after a dilation with scale factor k. A(1,2), B(3,-1), C(0,1); k = 3 A'(33, 23) = A'(9,6) B'(33, -13) = B'(9,-3) C'(03, 13) = C'(0,3) A(9,3), B(6,3), C(3,-3); k = -1/2 A'(9*(-1/2), 3*(-1/2)) = A'(-4.5, -1.5) B'(6*(-1/2), 3*(-1/2)) = B'(-3, -1.5) C'(3*(-1/2), -3*(-1/2)) = C'(-1.5, 1.5) 4.6 Similarity and Transformations Similar Figures have same shape angles but different lengths sizes If similar, all sides should have the same scale factor 1) Where is the image of ΔABC with vertices A(1,2), B(3,-1), and C(0,1) after the similarity transformation of Rotation: 180° and Dilation: (x,y) → (2x,2y)? A'(-1,-2) B'(-3,1) C'(0,-1) A''(-2,-4) B''(-6,2) C''(0,-2) 2) Describe the similarity transformation that maps ΔABC to ΔXYZ. A(-2,5), B(-2,2), C(-1,2) and X(3,3), Y(3,1), Z(2,1) These shapes are not similar. XY/AB = 3/1 XZ/AC = 1/1 These scale factors are not the same.