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Transformations

Reflections Rotations TranslationGlide

Reflections

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Misc Misc

100

Explain what an isometry is

Every pre-image is congruent to the image.

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500

Explain how to do a 270 degree rotation counterclockwise around the origin.

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Realize that 270 ccw is equal to 90 cw, so switch (x,y) to (y,x) and then take the original x

and make it negative which is (y, -x)

200

T/F: A rectangle has rotational symmetry and always has a symmetry line

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True

200

A regular hexagon has rotational symmetry and always has line symmetry.

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True

-100

Write the coordinate notation for a translation that moves horizontally 5 units to the right and vertically down 3 units.

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(x,y)– (x+5,y-3)

200

Which type of triangle has only one symmetry line: scalene, isosceles, equilateral?

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Isosceles

-100

A = (3,2); B = (5, -2); C=(0, -4). Draw triangle ABC and then the image after a reflection over the line x = 3.

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A’=(3,2) B’=(1,-2)

C’=(6,-4)

Steal 200

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400

Draw the pre-image and image after ABCD is rotated 90 counterclockwise about the origin. A = (2,4) B = (-1,8) C = (-4,4) D = (-2,0)

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A’=(-4,2); B’=(-8,-1);

C’=(-4,-4); D=(0, -2)

-200

In general, every point (x,y) is mapped onto what point when it’s reflected over the line y = x?

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(y,x)

300

In general, every point (x,y) is mapped onto what point when it’s reflected over the x-axis?

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(x, -y)

Lose 200

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1 4 7 3 41 ,3 ,2 ,3 ,3

5 5 10 10 5

500

Using the vector < -2, 8 >. Find the pre-image if A’(2,8).

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(4,0)

-200

Point B (3,2) is translated by the vector <-6, 2 > and then reflected over the y-axis. What is the final image?

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(3,4)

200

Draw the following picture on graph paper. A(-6,2) B(-8,-1) C(-10,3). A’(-3,-2) B’(-5,-5)

C’(-7,-1). A’’(3,-2) B’’(5,-5) C’’(7,-1). Describe the composition.

Translation:______________

Reflection:______________

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Translation: < 3,-4>

Reflection: y-axis

300

A=(2,1); B=(-2,4); C=(1,-8); A’=(10,-2); B’=(6,1); C’=(9,-11)

What is the vector describing the translation?

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< 8, -3 >

200

If a figure is rotated 176 degrees, what is the acute angle between the intersecting line?

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88 degrees

-300

If the acute angle between two lines is 38 degrees, what is the degree of the rotation?

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76 degrees

400

A=(8,2); B=(4,6); C=(-2,-3). Find the image of ABC after a glide reflection:

translation: (x,y) (x, y-5);

reflection: x = -2

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A’’(-12,3) B’’(-8,1)

C’’(-2,-8)

Steal 400

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-400

Take the pre-image points A(2,-4) & B(4,1) and rotate them 180 degrees about the origin. What are the image points?Then explain how you got your answer.

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A’(-2,4) B’(-4,-1). Take the negative of each coordinate.

200

The composite of two or more isometries is always….

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An isometry

200

T/F: A parallelogram has rotational symmetry and may have line symmetry.

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True

-100

When I say “write the component form” what type of symbols should be around your numbers?

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< >

600

T/F: A triangle always has a symmetry line

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False

500

(x,y) (x + 4, y + 6). The pre-image of A’ is A(-2,4). What is A’?

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(2,10)

200

How do you know if a figure has rotational symmetry?

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If you can rotate it 180 degrees or less and the

image falls on top of the pre-image.

-300

Explain what a symmetry line is

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The line you draw where when reflected, you will see

the exact same picture.

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