Reflections

University:
Princeton University
Course:
PHY 103 | General Physics I
Academic year:

2023
Views:

0

Pages:

5
Author:

Maria Medina

Reflections Def: The operation that moves an image around the coordinate plane is called a transformation. In any transformation, the original figure is called the preimage and the new figure achieved after the transformation is called the image. You can describe a transformation by writing: A → A' Reflections Def: A figure has a line of symmetry if the figure can be mapped onto itself by a reflection in the line. [Image of a heart with a line of symmetry drawn vertically] line of symmetry [Image of a heart with a line not in the middle] Not a line of symmetry Example: How many lines of symmetry do the following figures have? (a) [Image of an arrow] one (b) [Image of a regular hexagon with all lines of symmetry drawn] 6 (c) [Image of a circle] infinite In a reflection, we "flip" our pre-image over a line to get our new image. The line the figure is reflected over is called a line of symmetry. Rule: When a figure is reflected over the y-axis... the x coordinates change in sign. Example: The following points are vertices of a polygon being reflected over the y-axis. Find the image of each point. P = (3, 2) → P'' (-3, 2) Q = (-1, 5) → Q' (1, 5) R = (0, 3) → R' (0, 3) S = (½, 0) → S' (-½, 0) Rule: When a figure is reflected over the x-axis... y coordinates change sign Example: The following points are vertices of a polygon being reflected over the x-axis. Find the image of each point. P = (3, 2) → P' (3, -2) Q = (-1, 5) → Q' (-1, -5) R = (0, 3) → R' (0, -3) S = (½, 0) → S' (½, 0) Rule: When a figure is reflected over the line y = x... x and y switch Example: The following points are vertices of a polygon being reflected over the line y = x. Find the image of each point. P = (3, 2) → P' (2, 3) Q = (-1, 5) → Q' (5, -1) R = (0, 3) → R' (3, 0) S = (½, 0) → S' (0, ½) Rule: When a figure is reflected over the line y = -x... x and y switch and change signs Example: The following points are vertices of a polygon being reflected over the line y = -x. Find the image of each point. P = (3, 2) → P' (-2, -3) Q = (-1, 5) → Q' (-5, 1) R = (0, 3) → R' (-3, 0) S = (½, 0) → S' (0, -½) Example: Reflect the following: (a) Point A over the x-axis (2,3) → A'(2,-3) (b) Point C over the y-axis (-2, 1) → C'(2,1) (c) Point D over the line x = -2 (-4, -2) → D' (0,-2) (d) Point B over the line y = -1 (4, 2) → B'(4,-4) (e) Point E over the line x = 1 (5, -3) → E'(-3, -3) Compositions: Def: When two or more transformations are combined to form a single transformation, the result is a composition of transformations. (a) Reflect ABC over the y-axis line y = -2 [Diagram with the triangles ABC and A"B"C"] [Image labeled y-axis] (b) DE has endpoints D(-4, -4) and E(0, -4). Reflect DE over the line y = x then over x = 2 [Diagram showing the transformation] D(-4, -4) over y=x -> (-4,-4) over x=2 -> D"(8,-4) E(0, -4) over y=x -> (-4,0) over x=2 -> E"(8,0) [Diagram shows a line being reflected over y=x then x=2]