What is a glide reflection in geometry?

A glide reflection is a mirror reflection followed by a translation parallel to the mirror. Every glide reflection has a mirror line and translation distance.

What is a glide reflection example?

A typical example of glide reflection in everyday life would be the track of footprints left in the sand by a person walking on a beach. For any symmetry group containing some glide reflection symmetry, the translation vector of any glide reflection is one half of an element of the translation group.

How do you do glide reflections?

A glide reflection is just what it sounds like: You glide a figure (that’s just another way of saying slide or translate) and then reflect it over a reflecting line. Or you can reflect the figure first and then slide it; the result is the same either way. The footprints are glide reflections of each other.

Which represents a glide reflection?

Video quote: And a glide reflection is really a combination of two other transformations. It's a translation. So this L up here the figure ABC is it going to get slid around some way.

What is the difference between a glide reflection and a reflection?

“reflection” because similar things happen with a reflection in a mirror. A glide reflection combines a reflection with a translation along the direction of the mirror line. Glide reflections are the only type of symmetry that involve more than one step.

Is a glide reflection a rigid motion?

The other types of rigid motions are translations and glide reflections. These have no fixed points, which is why finite figures can’t have symmetries involving these. A vector is an arrow: it has length and direction.

What are the two transformations of a glide reflection?

To do a glide reflection, perform the two transformations, which are 1) reflection over the given line of reflection and 2) translation with respect to the given directions.

Is dilation a rigid motion?

A dilation is not considered a rigid motion because it does not preserve the distance between points.

Are glide reflections commutative?

A glide reflection is the composition of a reflection and a translation, where the line of reflection, m, is parallel to the directional vector line, v, of the translation. A glide reflection is commutative. Reversing the direction of the composition will not affect the outcome.

Can a glide reflection have two reflections?

And because you can produce the translation part with two reflections, you can achieve a glide reflection with three reflections. Some images are just one reflection away from their pre-images; other images (in translation and rotation problems) are two reflections away.

Can any reflection be replaced by a rotation?

Any reflection can be replaced by a rotation followed by a translation.

What is a vertical reflection?

Vertical Reflections



A vertical reflection is a reflection across the x -axis, given by the equation: y=−f(x) In this general equation, all y values are switched to their negative counterparts while the x values remain the same. The result is that the curve becomes flipped over the x -axis.

Is a horizontal reflection over the y-axis?

Another transformation that can be applied to a function is a reflection over the x- or y-axis. A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.

What are the 4 transformations in maths?

Translation, reflection, rotation, and dilation are the 4 types of transformations.

What are the 5 transformations?

These lessons help GCSE/IGCSE Maths students learn about different types of Transformation: Translation, Reflection, Rotation and Enlargement.

How do you rotate without tracing paper?

Video quote: Then we're going to draw a 90 degree angle. And then another line of exactly the same length. So these lines haven't changed lengths. And then we'll know exactly where we need to be on our image.

What does dilation mean in math?

Dilation Meaning in Math. Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape.

What is a vertical stretch?

What is a vertical stretch? Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. This results in the graph being pulled outward but retaining the input values (or x). When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis.

What is horizontal shrink?

A horizontal stretch or shrink by a factor of 1/k means that the point (x, y) on the graph of f(x) is transformed to the point (x/k, y) on the graph of g(x).

How do you reflect over the y-axis?

Video quote: If I'm going to reflect a point across the y-axis. Now. You can see you guys to the right X is positive right but if I'm going to take this point and reflect it over the y-axis.

Is f/x a vertical stretch?

A General Note: Vertical Stretches and Compressions



Given a function f(x) , a new function g(x)=af(x) g ( x ) = a f ( x ) , where a is a constant, is a vertical stretch or vertical compression of the function f(x) . If a>1 , then the graph will be stretched.

How do you do transformations on a graph?

5 Steps To Graph Function Transformations In Algebra

1. Identify The Parent Function. …
2. Reflect Over X-Axis or Y-Axis. …
3. Shift (Translate) Vertically or Horizontally. …
4. Vertical and Horizontal Stretches/Compressions. …
5. Plug in a couple of your coordinates into the parent function to double check your work.

What is a shrink in math?

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. • if k > 1, the graph of y = k•f (x) is the graph of f (x) vertically stretched by multiplying each of its y-coordinates by k.

What is the order for transformations?

Video quote: You can write horizontal translation first and then vertical. Or you can do vertical translation first and then horizontal. And on the other hand you can do vertical stretches.

How do you shift reflect and stretch on a graph?

Video quote: So remember adding and subtracting. Pick up and shift the wrath. Okay multiplying. And dividing stretch. Or compress and the key thing to remember is that if it's grouped with the X.

How do you vertically stretch a graph?

Video quote: It's outside the function that means it's vertical. And if it's a number greater than one it is a stretch. So I am taking each of my value each of my points on my graph.