Glide Reflections

In Glogpedia

by cmchaug
Last updated 5 years ago

Discipline:
Math
Subject:
Geometry
Grade:
9

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Glide Reflections

GLIDE REFLECTIONS

What are Glide Reflections?

Glide reflections are the combination of two trandofrmations: a reflection and a translation.

WATCH ME!

In a Glide Reflection...

- the line of reflection is parallel to the direction of the translation -the trasnformation is commutative (whether you translate or reflect first does not matter)-the image is an isometry (both translations and reflections are isometries)-distance, angle measures, parallelism, colinearity, and midpoints are preserved -orientation is not preserved

Examples

Reflection

Translation

Information Needed to Solve Glide Reflections:

-The line that you are reflecting over-The translation rule

Recalling Reflection Rules

Reflect over...

x-axis: (x,y) (x,-y)y-axis: (x,y) (-x,y)y=x: (x,y) (y,x)y=-x: (x,y) (-y,-x)

Steps for Solving a Glide Reflection

*Again, the order that you perform the transformations doesn't matter, in this case the reflection is done first*1. Identify the coordinates of the figure 2. Identify the line that you must reflect over & reflect the figure across that line (each point invidually) 3. Take the reflected figure and translate it according to the rule that the question states (each point individually)

Sample Question

Given △ABC, graph and label the following compostition: T <-5,0> ° R x-axis1. A(5,5) B(1,3) C(2,1)2. The reflection is over the x-axis [ (x,y) becomes (x,-y) ]A(5,5) ➝ (5,-5) B(1,3) ➝ (1,-3) C(2,1) ➝ (2,-1)3. The translation rule is <-5,0> so... (x-5, y) A(5,-5) ➝ (0,-5) B(1,-3) ➝ (-4,-3) C(2,-1) ➝ (-3,-1)Is the image a glide reflection of △ABC? Yes because it is a composition of a reflection and a translation.Would the answer change if the translation occurred first? No because glide reflections are commutative.


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