How Do You Graph a Glide Reflection?

Note:

When you graph a composition of two transformations, you have to be very careful to perform all the steps in the right order! Watch this tutorial to see how to graph a glide reflection.

Keywords:

problem
graph
glide
reflection
isometry
translation
composition
isometries

Background Tutorials

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
- What is the X-Coordinate?
  
  Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the x-coordinate in an ordered pair!
- What is the Y-Coordinate?
  
  Ordered pairs are a crucial part of graphing, but you need to know how to identify the coordinates in an ordered pair if you're going to plot it on a coordinate plane. In this tutorial, you'll see how to identify the y-coordinate in an ordered pair!
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
- What is an Ordered Pair?
  
  Ordered pairs are a fundamental part of graphing. Ordered pairs make up functions on a graph, and very often, you need to plot ordered pairs in order to see what the graph of a function looks like. This tutorial will introduce you to ordered pairs!
Lines are taken to lines, and line segments to line segments of the same length.
- What is a Translation?
  
  Ever slide something across a table? If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples. Take a look!
- What is a Transformation?
  
  Transformations can be really fun! They allow you to change or move a figure. In this tutorial, learn about all the different kinds of transformations!
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
- What is a Reflection?
  
  When you look in the mirror, you see your reflection. In math, you can create mirror images of figures by reflecting them over a given line. This tutorial introduces you to reflections and shows you some examples of reflections. Take a look!
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- How Do You Use Coordinates to Translate a Figure Horizontally?
  
  Translating a figure on the coordinate plane is easier than you might think! This tutorial shows you how to translate coordinates from the original figure. Then, simply connect the points to create your new figure. This tutorial shows you how!
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
- What is a Triangle?
  
  You can't learn everything about math without dealing with triangles. Did you know that there are different types of triangles? Check out this tutorial, and learn about triangles and their different types!
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
- What is an Image?
  
  Just about everything in math has a name! Did you know that when you're dealing with transformations, the new figure you get is called an image? Check out this tutorial and learn about this math term!

How Do You Graph a Glide Reflection?

How Do You Graph a Glide Reflection?

Note:

Keywords:

Background Tutorials

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

Lines are taken to lines, and line segments to line segments of the same length.

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.