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

2019
Views:

300

Pages:

3
Author:

MarleyC

Chapter 4 Study Guide Geometry 4.1 Translations Graph ΔABC with vertices A(1, 2), B(3, -1), and C(0, 4) and its image after the translation (x, y) → (x + 5, y - 3) (x, y) → (x + 2, y + 2) Translation: (x, y) → (x + 4, y + 1) Graph ΔABC and its image after the composition. A = original A' = first transformation A'' = second transformation Always label your points 4.2 Reflections Graph ΔABC with vertices A(1, 2), B(3, -1), and C(0, 4) and its image after the reflection in the given line. X-axis y = -x x = 2 Rules for (a, b) x-axis: (a, -b) y-axis: (-a, b) y = x: (b, a) y = -x: (-b, -a) How many lines of symmetry does the figure have? one five none Line of Symmetry divides into two identical parts 4.3 Rotations Graph ΔABC with vertices A(1, 2), B(3, -1), and C(0, 4) and its image after the rotation of the given number of degrees about the origin. 180° 270° 90° Determine whether the figure has rotational symmetry. If so, describe any rotation that maps the figure onto itself. none yes, 180° yes, 150° Rules for (a, b) 90°: (-b, a) 180°: (-a, -b) 270°: (b, -a) Rotational Symmetry when you can spin an object at the center and get the same thing 180° or less Graph ΔABC and its image after the composition. Rotate: 90° Translation: (x, y) → (x + 3, y) Reflection in x-axis Translation: (x, y) → (x - 1, y + 3) Reflection in y = x 4.4 Congruence and Transformations Describe a congruence transformation that maps ΔABC to ΔXYZ. A(5, 2), B(2, 2), C(1, 7) and X(-4, -5), Y(-1, -5), Z(-1, 0) Composition (usually more than one way to state it) Translation (x, y) → (x + 5, y) Reflection on x = 1 If you perform two reflections over intersecting lines that are 36° apart, what is the angle of rotation for the figure? 72° 4.4 Dilations Graph the triangle and its image after a dilation with scale factor k. A(1, 2), B(3, -1), C(0, 4); k = 3 [A'(3, 6), B'(9, -3), C'(0, 12)] A(9, 3), B(6, 3), C(3, 3); k = 1/2 [A'(-4.5, 1.5), B'(-3, -1.5), C'(-1.5, 1.5)] 4.6 Similarity and Transformations Where is the image of ΔABC with vertices A(1, 2), B(3, -1), and C(0, 4) after the similarity transformation of Rotation: 180° and Dilation: (x, y) → (2x, 2y)? [A"(-2, -4), B"(-6, 2), C"(0, -8)] Describe the similarity transformation that maps ΔABC to ΔA'B'C'. A(-1, 2), B(-2, 2), C(-1, 7) and A'(3, 3), B'(2, 1), C'(2, 7) Not Similar If similar, all sides should be the same scale factor [\frac{\overline{AB}}{\overline{A'B'}} = \frac{1}{2}] [\frac{\overline{BC}}{\overline{B'C'}} = \frac{1}{1} = (1)] These scale factors are not the same