University:
High School
Course:
High School Geometry
Academic year:

2019
Views:

101

Pages:

4
Author:

sezylipz2kissf8

4.1 Transformations 1. Graph ∆ABC with vertices A(1, 2), B(3, 1), and C(2, 4) and image after the composition. Translation: T<3, -2> Rotation: 90° clockwise about the origin 2. Graph ∆ABC with vertices A(1, 2), B(3, 1), and C(2, 4) and image after the composition. Reflection: over the x-axis Translation: T<4, -1> 3. Graph ∆ABC with vertices A(1, 2), B(3, 1), and C(2, 4) and image after the composition. Rotation: 90° counterclockwise about the origin Translation: T<-4, 5> 4.2 Reflections 1. Graph ∆ABC with vertices A(1, 2), B(3, 1), and C(2, 4) and image after the reflection. Reflection: over the y-axis 2. Graph ∆ABC with vertices A(1, 2), B(3, 1), and C(2, 4) and image after the reflection. Reflection: over the line y = x 4.3 Symmetry 1. Determine whether the object has rotational symmetry and if it does, state the order of rotational symmetry. 4.4 Congruence 1. Use coordinate notation to describe the transformation. [Diagram of a triangle and its image] 2. Describe the composition of transformations that maps ∆ABC onto ∆A'B'C'. ∆ABC: A(5, 2), B(1, 2), C(2, 7) ∆A'B'C': A'(2, 0), B(-2, 0), C(-1, 5) 3. Determine the line of reflection when reflecting the pre-image onto the image. [Diagram of a triangle and its image] 72° 4.1 Translations 1. Graph ∆ABC with vertices A(1, 2), B(3, -1), and C(2, 3) and its image after the translation. * (x, y) → (x + 1, y - 3) 2. Graph ∆ABC with vertices A(1, 2), B(3, -1), and C(2, 3) and its image after the translation. * <4, 2> 3. Graph ∆ABC with vertices A(5, 3), B(7, 0), and C(7, 5) and its image after the composition. * Translation: (x, y) → (x + 2, y + 1) * Translation: (x, y) → (x - 2, y - 5) 4.2 Reflections 1. Graph ∆ABC with vertices A(1, 2), B(3, -1), and C(2, 3) and its image after the reflection in the given line. * x-axis 2. Graph ∆ABC with vertices A(1, 2), B(3, -1), and C(2, 3) and its image after the reflection in the given line. * y = x 3. Graph ∆ABC and its image after the composition. * Translation: (x, y) → (x + 3, y) * Reflection: in y-axis 4.3 Rotations "turn" the figure around a point... usually the origin... in a counter-clockwise direction. Rules for (a, b) 90°: (-b, a) 180°: (-a, -b) 270°: (b, -a) Graph ∆ABC with vertices A(1, 2), B(3, -1), and C(3, 4) and its image after the rotation of the given number of degrees about the origin. 1. 180° A'(-1, -2) B'(-3, 1) C'(-3, -4) 2. 270° A'(2, -1) B'(-1, -3) C'(-4, 3) Graph ∆ABC and its image after the composition. 7. Rotate: 90° A'(-2, 1) B'(1, 3) C'(-4, 3) Translation: (x, y) → (x + 1, y + 3) A'(-1, 4) B'(2, 6) C'(-3, 6) 4.2 & 4.3 Symmetry Line Symmetry divides objects into two identical parts Rotational Symmetry when you can spin an object at the center and get the same thing 180° or less Determine whether the object has reflectional symmetry and whether it has rotational symmetry. Identify all lines of symmetry and angles of rotation. 1. 1 [Diagram of a shape with one line of symmetry] 1 line of symmetry no rotational symmetry 2. [Diagram of a shape with five lines of symmetry] 5 lines of symmetry rotational symmetry at 72°, 144°, 216°, 288°, 360° 360°/5 = 72° 3. [Diagram of a shape with no lines of symmetry] No lines of symmetry rotational symmetry at 180° 360°/2 = 180°