# which composition of transformations will create a pair of similar, not congruent triangles? a rotation, then a reflection a translation, then a rotation a reflection, then a translation a rotation, then a dilation

### James

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get which composition of transformations will create a pair of similar, not congruent triangles? a rotation, then a reflection a translation, then a rotation a reflection, then a translation a rotation, then a dilation from EN Bilgi.

## Composition of Transformations (Isometries)

**Composition (Sequences) of Transformations**MathBitsNotebook.com

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When two or more transformations are combined to form a new transformation, the result is called a composition of transformations, or a sequence of transformations. In a composition, one transformation produces an image upon which the other transformation is then performed.

In Algebra 2, you will see "composition of functions" which will work in this same manner.

The symbol for a composition of transformations (or functions) is an open circle.

A notation such as is read as:

"a translation of (x, y) → (x + 1, y + 5) **after** a reflection in the line y = x".

You may also see the notation written as .

This process must be done from right to left ()!!

Composition of transformations is not commutative.

As the graphs below show, if the transformation is read from left to right,

the result will NOT be the same as reading from right to left.

Let's look at some special situations involving combinations:

In certain cases, a combination of transformations may be **renamed** by a single transformation.

Example:

The combination of a line reflection in the y-axis, followed by a line reflection in the x-axis, can be renamed as a single transformation of a rotation of 180º (in the origin).

It is not possible to rename all compositions of transformations with **one** transformation, however:

Any translation or rotation can be expressed as the composition of two reflections.

A composition of reflections **over two parallel lines** is equivalent to a translation.

(May also be over any even number of parallel lines.)

Example: Given a || b, and pre-image ΔABC, where parallel lines are vertical.

Look carefully in this situation to see which of the parallel lines will be the first line of reflection. Do not assume the parallel line nearest the pre-image (as in this example) will always be used first.

It can be seen from the diagram, that ΔA''B''C'' could also be a horizontal translation of ΔABC. The horizontal distance of the translation will be twice the width between the vertical parallel lines.

The parallel lines may be vertical (as seen in this example), horizontal or slanted.

The composition of reflections** over two intersecting lines** is equivalent to a rotation.

The center of rotation is the intersection point of the lines.

Example: Given two lines, a and b, intersecting at point P, and pre-image ΔABC.

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).

Remember that, by convention, the angles are read in a counterclockwise direction. You may also apply this rule to negative angles (clockwise).

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.

Example:

A glide reflection is commutative. Reversing the direction of the composition will not affect the outcome.

Footprints are an example of several glide reflections. In the diagram at the left, you are seeing the original "step" on the left foot, followed by the "step" on the right foot, which is the "result" of the glide reflection. When compared to the diagram of the triangles, shown above, you are not seeing ΔA'B'C' (reflection) in the footprints.

The composition of two rotations from the same center, is a rotation whose degree of rotation equals the sum of the degree rotations of the two initial rotations.

Example:

Note that CP = CP' = CP'', as they are radii of circle C.

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**copyright violation**and is not considered "fair use" for educators. Please read the "Terms of Use".

## Which composition of transformations will create a

Answer: The answer is a rotation, then a dilation.

Math Resources/ algebra/ equation/

## Which composition of transformations will create a pair of similar, not congruent triangles?a rotation, then a reflectiona translation, then a rotationa reflection, then a translationa rotation, then a dilation

Question

### Gauthmathier1744

Grade 12 · 2021-07-15

YES! We solved the question!

Check the full answer on App Gauthmath

Which composition of transformations will create a pair of similar, not congruent triangles?

a rotation, then a reflection

a translation, then a rotation

a reflection, then a translation

a rotation, then a dilation

Good Question (197) Answer 5 (461) votes Write neatly (85) Correct answer (74) Help me a lot (71) Detailed steps (42)

Excellent Handwriting (23)

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### Gauthmathier6713

Grade 12 · 2021-07-15

Answer

The answer is a rotation, then a dilation

Thanks (79)

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## Chapter 12 Flashcards

Start studying Chapter 12. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Chapter 12

5.0 2 Reviews isometry

Click card to see definition 👆

A transformation that does not change the shape or size of a figure. Ex: reflections, translations, and rotations

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Reflection

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A transformation that moves a figure the preimage by flipping it across a line.

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1/37 Created by dmacbernardsville

### Terms in this set (37)

isometry

A transformation that does not change the shape or size of a figure. Ex: reflections, translations, and rotations

Reflection

A transformation that moves a figure the preimage by flipping it across a line.

Image

The reflected figure that is congruent to the original PREimage.

Rigid motions

What isometrys are also called

reflections

A reflection is a transformation across a line called the line of reflection, so that the line of reflection is the perpendicular bisector of each segment joining each point and its image.

reflections across the x-axis

(x,y) to (x,-y)

reflections across the y axis

(x,y) to (-x,y)

reflections across y=x

(x,y) to (y,x)\ Translation

A transformation is a transformation where all points of a figure are moved the same distance in the same direction. A translation is an isometry , so the image of a translated figure is congruent to the preimage.

Rotation

A transformation that turns a figure around a fixed point, called the center of rotation. A rotation is an isometry so the image is congruent to the preimage.

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