Can A Translation Be Replaced By Two Reflections? - Fixanswer

The compositions of reflections over parallel lines theorem states two things: If we perform a composition

of two reflections over two parallel lines

, the result is equivalent to a single translation transformation of the original object.

Can a rotation be replaced by a reflection?

Every rotation of the plane can be replaced by the composition of

two reflections through lines

.

Can translations be reflections?

A reflection is the flipping of a point or figure over a line of reflection (the mirror line). … And a translation is a scenario where every point in a figure

is moved the

exact same distance and in the same exact direction, without being rotated, reflected, or resized.

What is the orientation of a figure?

Orientation is

the relative arrangements of points after a transformation or after traveling around a geometric figure

. Orientation is sorted into clockwise and counterclockwise in terms of how the points align. Reverse orientation means that the points are opposite of the original shape.

Does order of reflections for a composition of two reflections in parallel lines matter?

Reflection over the Axes Theorem: If you compose two reflections over each axis, then the final image is a rotation of begin{align*}180^circend{align*} of the original. With this particular composition,

order does not matter

.

Why do two reflections rotate?

The composition of reflections over two intersecting lines is

equivalent to a rotation

. … The double reflections are equivalent to a rotation of the pre-image about point P of an angle of rotation which is twice the angle formed between the intersecting lines (theta).

What is the difference between translation reflection and rotation?

Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape. Translation is

sliding

a figure in any direction without changing its size, shape or orientation.

Is a 180 degree rotation the same as a reflection?

The reflection is the same as rotating

the figure 180 degrees. The two motions (transformations) can't be compared, since a rotation can be from and to any angle, but a reflection can only be horizontal or vertical.

What is translation reflection?

Translation is when we slide a figure in any direction. Reflection is

when we flip a figure over a line

.

What stays the same after a reflection?

When you reflect a point across the x-axis,

the x-coordinate remains the same

, but the y-coordinate is transformed into its opposite (its sign is changed). If you forget the rules for reflections when graphing, simply fold your paper along the x-axis (the line of reflection) to see where the new figure will be located.

What is object orientation?

In geometry, the orientation, angular position, attitude, or direction of an object such as a line, plane or rigid body is

part of the description of how it is placed in the space it occupies

.

Does a reflection flip an object?

A reflection is colloquially known as a flip because it does the same thing a mirror does −

flips an object over a line or point or plane into an image

. … The same holds for sets of points such as lines and planes.

How do you do transformations on Desmos?

Graph Transformations. Starting at

y=2f(x)

, click on the circle to reveal a new graph. Describe the transformation. Click again to remove and try the next function.

What is transformation golf?

Transforming Shapes. In this activity, students use their existing understanding

of translations, reflections, and rotations

to complete a round of transformation golf. For each challenge, their task is the same: Use one or more transformations to transform the pre-image onto the image.

Do reflections preserve orientation?

Reflection does not preserve orientation

. Dilation (scaling), rotation and translation (shift) do preserve it.

What is the composition of two reflections?

The composition of two reflections in non-parallel lines is

a rotation about the intersection point of the lines by the angle equal to doubled angle between the lines.

Does reflection preserve distance?

The mirror line is the perpendicular bisector of the line segment joining an object point and its image point. the perpendicular distance of the object point to the mirror is equal to the perpendicular distance of its image from the mirror line.

Reflection preserve the distance between two points

.

Does orientation change in translation?

A translation is when a geometric figure slides up, down, left or right on the coordinate plane. The figure moves its location, but

doesn't change its orientation

. It also doesn't change its size or shape. When you perform translations, you slide a figure left or right, up or down.

Are reflections commutative?

In general,

two reflections do not commute

; a reflection and a rotation do not commute; two rotations do not commute; a translation and a reflection do not commute; a translation and a rotation do not commute. Two translations do commute, and two rotations pivoting around the same point commute.

What is a combination of two reflections?

Combination of Two Reflection. A

point or object once reflected can further be reflected to form a new image

. The axes of these reflections may be parallel to each other or they intersect each other at a point. So, there are two cases for the combination of two reflections.

What one transformation is the same as a reflection over two parallel lines?

A composition of reflections over parallel lines has the same effect as

a translation

(twice the distance between the parallel lines). A composition of reflections over intersecting lines is the same as a rotation (twice the measure of the angle formed by the lines).

Does reflection order matter?

If two or more of the transformations have a vertical effect on the graph, the order of those transformations

will most likely affect the

graph. If two or more of the transformations have a horizontal effect on the graph, the order of those transformations will most likely affect the graph.

Which translation is equivalent to this double reflection?

A DOUBLE REFLECTION OVER PARALLEL LINES IS A TRANSLATION. THE TRANSLATION IS

DOUBLE THE DISTANCE B/TW THE PARALLEL LINES

. x=1 is a vertical line and x=-2 is vertical.

Are glide reflections commutative?

For example, a glide reflection is such

commutative composition of translation and reflection

, with reflection line parallel to the translation axis.

What are translations reflections and rotations are all known as?

A

transformation

is an operation that maps an original figure onto a new figure called the image. … Notes of transformations, including, translations, reflections, rotations and dilation.

How do you tell if a transformation is a reflection?

A reflection swaps all of the x or y values across the x or y -axis, respectively. …
A vertical reflection is given by the equation y=−f(x) y = − f ( x ) and results in the curve being “reflected” across the x-axis.

What is 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.

How many reflection lines are there in a rotation?

Two reflections

make a rotation.

How many rotations make a reflection?

This means that if the symbol is rotated from the center (center of rotation) 120 degrees, it will look the same as the original picture. It will take

three spins

to get back to the original image. Reflection can be thought of as a mirror image.

What transformation is non rigid?

Non-rigid transformations change the size or shape of objects.

Resizing (stretching horizontally, vertically, or both ways)

is a non-rigid transformation.

What are the properties of reflections?

Basic Properties of Reflections: (Reflection 1) A reflection maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle. (Reflection 2)

A reflection preserves lengths of segments

. (Reflection 3) A reflection preserves measures of angles.

What is difference between association and aggregation?

Aggregation Association	Diamond shape structure is used next to the assembly class. Line segment is used between the components or the class

What is object orientation explain any two object-oriented themes?

Object Oriented: It means that

we organize software as a collection of discrete objects that incorporate both data structure and behavior

. It includes four aspects: 1. Identity: – It means that data is quantized into discrete, distinguishable entities called object.

What OOP in Java?

Java – What is OOP? OOP stands for

Object-Oriented Programming

. Procedural programming is about writing procedures or methods that perform operations on the data, while object-oriented programming is about creating objects that contain both data and methods.