4.4 Congruence and Transformations

​4.4 Congruence and Transformations

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" REAL TRANSFORMATIONS require real honesty. If you want to move forward, get real with yourself."

​

-Unknown

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Properties of Sequences of Rigid Motions

• Size and shape stay the same.

• Angle measures stay the same.

• Area and perimeter stay the same.

• Parallel segments or lines stay parallel.

• Pre-image and image are congruent.

Multiple Choice

Which of the following describes the sequence of transformations shown? #1

• Reflect across the x-axis and then rotate -90 degrees around the origin

• Rotate -90 degrees around the origin and then translate down.

• Reflect across the x-axis and then reflect across the y-axis.

• Translate up and then rotate 90 degrees about the origin.

Multiple Choice

Which of the following are congruence transformations? #3

• Rotations

• Translations

• Reflections

• All Three

Multiple Choice

Which of the following is a rigid motion? #24

• $$\left(x,y\right)\rightarrow\left(3x,y\right)\rightarrow\left(x+5,y-8\right)\rightarrow\left(-x,y\right)$$

• $$\left(x,y\right)\rightarrow\left(-x,-y\right)\rightarrow\left(x-3,y+8\right)\rightarrow\left(-x,y\right)$$

• $$\left(x,y\right)\rightarrow\left(-y,x\right)\rightarrow\left(-2x,2y\right)\rightarrow\left(-x,y\right)$$

• $$\left(x,y\right)\rightarrow\left(\frac{1}{2}x,y\right)\rightarrow\left(x+5,y-8\right)$$

Multiple Choice

Which sequence of transformations maps

Quadrilateral WXYZ onto Quadrilateral W"X"Y"Z"? #22

• A 90° counter-clockwise rotation, then a translation.

• A reflection across the y-axis, then a reflection across the x-axis.

• A translation, then a reflection across the y-axis.

• A translation, then a reflection across the x-axis.

Multiple Choice

Which sequence of transformations maps the green triangle to the red triangle to the blue triangle? (NOT ON THE PACKET)

• A rotation, then a translation.

• A translation, then a rotation.

• A translation, then a reflection.

• A rotation, then a reflection.

Multiple Choice

What is the image of point ( 4,2) after the composition of transformations defined by reflection over y=x, (x, y) → (y, x), and a 90 degree counter clockwise rotation around the origin, (x, y) → (–y, x) ? #11

• (-4, 2)

• (4, -2)

• (-4, -2)

• (2, -4)

Multiple Choice

What is the ordered pair for the final location of P( -7, 3) after this series of transformations? $$\left(x,y\right)\rightarrow\left(x,\ y+3\right)$$  then rotated  $$90\degree$$  clockwise about the origin. #25

• $$P'\left(-7,\ 6\right)$$  

• $$P'\left(-7,\ -6\right)$$  

• $$P'\left(6,\ -7\right)$$  

• $$P'\left(6,\ 7\right)$$  

Multiple Choice

Figure WXYZ is transformed using the rule (x, y) → (x -4, y +2) then a reflection over the y-axis, (x, y) → (–x, y). #12

Point W of the pre-image is at (1, 6).

What are the coordinates of point W" on the final image?

• (–5, 8)

• (–3, –8)

• (5, –8)

• (3, 8)

Multiple Choice

Identify the sequences of transformations from the red image to the blue image.  #26

• reflection over the x-axis then rotation of $$90\degree$$ counterclockwise

• reflection over the y-axis then rotation ofundefined counterclockwise

• translation of 2 units to the right then rotation ofundefinedclockwise

• rotation of $$180\degree$$  counterclockwise

Multiple Select

Which transformation was performed on the new image? #27

• reflect over the x-axis, then rotate 90

• reflect over the y-axis, then translate

• rotate 90, then translate

• reflect over the x-axis, then translate

Multiple Select

Which transformation was performed on the new image? Select all that apply. #28

• rotate 90 cw

• translate: 4 units right and 5 units down

• reflect over x-axis

• rotate 270 cw

• reflect over y-axis

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Multiple Choice

$$Scale\ Factor=\frac{Image}{\Pr e-Image}$$  Which could be the rule used to dilate ABC to A'B'C'? #16

• (5x, 5y)

• (3x, 3y)

• (1/3 x, 1/3 y)

• (2x, 2y)

Multiple Choice

Enlargement or reduction? Find the scale factor! #14

• It's a reduction; the scale factor is 2.

• It's an enlargement; the scale factor is 2.

• It's an enlargement; the scale factor is 1/2.

• It's a reduction; the scale factor is 1/2.

Multiple Choice

A triangle has vertices with coordinates (2,0), (3, -1), and (-2,-5). If the triangle is dilated by a scale factor of 3 with the origin as the center of dilation, what are the coordinates of the vertices of the image?

• (5,3), (6,2), (1,-2)

• (6,0), (9,-3), (-6,-15)

• (2/3,0), (1,-1/3), (-2/3,-5/3)

• (-1,-3), (0,-4), (-5,-8)

Multiple Choice

Dilate the figure by a scale factor of 3 with the origin as the center of dilation. What are the coordinates of the image?

A(3,3) B(6,6) C(9,3)

• A'(9,9) B'(18,18) C'(27,9)

• A'(6,6) B'(9,9) C'(12,6)

• A'(0,0) B'(3,3) C'(6,0)

• A'(1,1) B'(2,2) C'(3,1)