Isometries-100

Isometries Rotations Translations Compositions

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500 500 500 500

Isometries-100home answer

What is the definition of an isometry? Give three examples of isometries.

Isometries-100Answer

Isometry: a transformation that perseveres length, angle measure, parallel lines, etc.

ex. Reflections

Rotations

Translations

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Isometries-200Which of the following is not a rotation of

?

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a) b)c)

Isometries-200Answer

c)

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Isometries-300

True or false?

1) Transformations that are not isometries are called rigid transformations.

2) Flips, turns and slides are nicknames for reflections, rotations and translations

3) Isometries preserve angle measures and parallel lines

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Isometries-300Answer

1. False

2. True

3. True

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Isometries-400Find the value of each variable if the given

transformation is an isometry

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a°50° b°

2c+3

7

12

4d50°

Isometries-400Answer

a=90° c=2

2c+3=7

2c=4

c=2

b=40° d=3

180-90-50 4d=12

90-50 d=3

40

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Isometries-500

Is the given transformation an isometry?

ABC XYZ

A=(-4,2) X=(2,2)

B=(-1,4) Y=(4,-1)

C=(-1,1) Z=(1,-1)

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Isometries-500Answer

YesUse the distance formula to compare the side lengthsAB=√(-4+1)²+(2-4)² BC=√(-1+1)²+(4-1)² AC=√(-4+1)²+(2-

1)² =√(-3)²+(-2)² =√(0)²+(3)² =√(-3)²+(1)² =√9+4 =√9 =√9+1 =√13 =3 =√10

XY=√(2-4)²+(2+1)² YZ=√(4-1)²+(-1+1)² XZ=√(2-1)²+(2+1)² =√(-2)²+(3) ² =√(3)²+(0)² =√(1)²+(3)² =√4+9 =√9 =√1+9 =√13 =3 =√10AB=XY BC=YZ AC=XZ

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Rotations-100home answer

Does this figure have rotational symmetry? If so, describe the rotation that maps the figure onto itself.

Rotations-100Answer

Yes, the star does have rotational symmetry. To map the figure onto itself, you could rotate the object 72° or 144°.

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Rotations-200

A=(2,-3) All=(-3,-2)

If A was rotated clockwise around the origin, what was the angle of rotation?

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Rotations-200Answer

90°

In a 90° clockwise rotation, (x,y) (y,-x)

If you use that information, you can substitute in (2,-3) to get (-2,-3), which are the coordinates of the given pre-image and image

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Rotations-300home answer

138°

.A.Al

.All

What is the measure of the angle of rotation?

mK

Rotations-300Answer

84 ° When you reflect a figure over line k then over line m, the

angle of rotation is 2x (x=the measure of the acute angle formed by k and m)

So, x=180-138

x=42

2(42)=84°

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Rotations-400

Rotate (7,-2) 90°clockwise around the origin. Name the point of the image. Do the same for 180° and 270° clockwise.

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Rotations-400Answer

90°=(-2, -7) because (x,y) (y,-x)

180°=(-7,2) because (x,y) (-x,-y)

270°=(2,7) because (x,y) (-y,x)

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Rotations-500home answer

Find the values of all the variables

5

5c

10

2d+2

8

4b

a° 65°

Rotations-500Answer

a=130° c=1

a=2(65) 5c=5

a=130 c=1

b=2 d=4

4b=8 2d+2=10

b=2 2d=8

d=4

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Translations-100

Reflect AB, A=(3,-3) B= (2,-4), over y=1. What are the coordinates of Al and Bl

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Translations-100Answer

Al=(3,5) Bl=(2,-6)

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Translation-200

Find the other endpoint using the following vectors.

1.(-4,0) vector <2,-3>

2. (5, -2) vector <5,1>

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Translation-200Answer

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1.(-2,-3)(-4+2,0-3)(-2,-3)

2. (10,-1)(5+5,-2+1)(10,-1)

Translation-300home answer

Use the following coordinate notation to find the other endpoint.

(x, y) (x+2, y-3)

1.(1,4)

2. (-3, -1)

Translation-300Answer

1. (3,1)

(1+2,4-3)

(3,1)

2. (-1,-4)

(-3+2,-1-3)

(-1,-4)

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Translation-400

A translation of AB is described by vector PQ<2,-5>. Find the value of each variable.

A(w-5,-3)Al(10,x-1)

B(z,3y+1)Bl(5,5)

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Translation-400Answer

w=10 y=3w-5+2=10 3y+1-5=5w-3=10 3y-4=5w=13 3y=9

x=-7 y=3-3-5=x-1 z=3-8=x-1 z+2=5-7=x z=3

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Translation-500

Write the equation for the line of reflection

A=(2,3) B=(6,-1)

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Translation-500Answer

y= x-3Explanation: (2,3) (6,-1) Slope= (3+1)=-1 midpoint=(6+2 3-1)= (4,1)

(2-6) 2 , 2Perp. Line slope=1 y=1x+b1=1(4)+b1=4+b-3=by=x-3

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Compositions-100

What is a composition? What is a glide reflection?

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Compositions-100Answer

A composition is when 2 or more transformations are combined to form a single transformation

A glide reflection is a transformation in which every point P is mapped onto Pll by the following 2 steps

-a translation that maps P onto Pl

-a reflection in line k such that the line of translation is parallel to reflection line k

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Compositions-200

When you switch the order of transformations, does it affect the final image? In what cases?

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Compostitions-200Answer

In a composition, it does affect the final image, but it does not in a glide reflection.

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Compostitions-300

Rotate A(3,2) 90° about the origin and reflect over the x-axis.

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Compositions-300Answer

Al (2,-3)

All(2,3)

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Compositions-400

Sketch the image of AB, A(4,2) B(7,0), after a composition using the given transformations (in the given order)

Translation:

(x,y) (x-4,y+2)

Rotation:

270° clockwise about the origin

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Compositions-400 Answer

Translation:

A(0,4) B(3,2)

Rotation:

A(-4,0) B(-2,3)

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Compositions-500

Sketch the image of A (-5,2) after translating it using vector <3,-4> and reflecting over x=4

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Compositions-500Answer

After translation: Al(-2,-2)

After reflection: All(10,-2)

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