Rotations and Sequences of Transformations

Rotations

Let's start with some review questions...

Multiple Choice

Triangle ABC is translated 6 units to the right to form triangle DEF. What are the coordinates for point D in the transformed triangle?

• (4, -4)

• (0, 4)

• (6, -4)

• (0, -4)

Multiple Choice

The pentagon shown below is reflected over the y-axis and then translated 2 units up. Which option shows this transformation?

Multiple Choice

Triangle ABC is translated to create triangle A'B'C'. Write a rule describing this translation.

• (x - 4, y + 3)

• (x + 4, y - 3)

• (x + 3, y - 4)

• (x - 3, y + 4)

Multiple Choice

Triangle B is rotated 90° counterclockwise with the origin as the center of rotation to create a new figure. Which rule describes this transformation?

• (x,y)→(y, -x)

• (x,y)→(x,y)

• (x,y)→(-x,-y)

• (x,y)→(-y,x)

Multiple Choice

Triangle A is rotated 270° counterclockwise with the origin as the center of rotation to create a new figure. Which rule describes rotating 270° counterclockwise?

• (x,y)→(y, -x)

• (x,y)→(x,y)

• (x,y)→(-y,x)

• (x,y)→(-x,-y)

Multiple Choice

Which of the following best describes the rotation shown?

• △S’T’U’ is a 90° rotation of △STU about point P.

• △S’T’U’ is a 180° rotation of △STU about point P.

• △S’T’U’ is a 270° rotation of △STU about point P.

• △S’T’U’ is a 360° rotation of △STU about point P.

Multiple Choice

The coordinates of the vertices of triangle CDE are C(3, –2), D(5, 2), and E(7, 0). The figure is rotated 90° about the origin. What is the coordinate of Point C'?

• (-3, 2)

• (2, 3)

• (-2, 3)

• (3, -2)

Multiple Choice

Triangle A is rotated 90° clockwise with the origin as the center of rotation to create a new figure. Which triangle shows the new location?

• A

• B

• C

• D

Multiple Choice

Rotate the point (-5,8) around the origin 270 degrees counterclockwise. State the image of the point.

• (-8,5)

• (8,-5)

• (8,5)

• (5,-8)

Sequences of Transformations (Rigid Motions)

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.

Sequences...

Sequences of transformations are performed by doing each transformation in the order listed. Perform the first transformation on the pre-image and each transformation after that on the image created by the previous transformation. When written as transformation rules, perform transformations from right to left.

Example

    

Square ABCD is rotated 90° counterclockwise and then reflected over the y-axis to form square A'B'C'D'.

Multiple Choice

What sequence of transformations maps the red parallelogram to the green parallelogram?

• A translation followed by a reflection.

• A rotation followed by a translation.

• A reflection followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

Which sequence could be used to transform hexagon C to hexagon D?

• Translation 4 left and 2 down

• a reflection over the x-axis and a translation 6 units right

• a reflection over the y-axis and a translation 2 units down

• a counter-clockwise rotation of 90 degrees about the origin

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflection followed by a rotation.

• Rotation followed by a translation.

• Reflection across the x-axis followed by a reflection across the y-axis.

• Translation followed by a rotation.

Multiple Choice

What are the series of rigid motions that would map ∆ABC onto ∆A''B''C''?

• a reflection followed by a rotation
• a reflection followed by a translation
• a translation followed by a rotation
• a translation followed by a reflection

Multiple Choice

Reflect triangle ABC across the y-axis:

A (2, 5) B (-3, 1) C (-3, -3)

• A' (-2, 5) B' (3, 1) C' (3, -3)

• A' (2, -5) B' (-3, -1) C' (-3, 3)

• A' (-2, -5) B' (-3, 1) C' (3, 3)

• A' (-2, 5) B' (3, -1) C' (3, -3)

Multiple Choice

Given the point A at (-6, -2), where would the image be after the translation T_{(-4, 2)}?

• (-2, 4)

• (-10, 0)

• (2, 0)

• (-8, -4)

Multiple Choice

What are the coordinates of point A' , the image of point A(-4, 1)  after the composite transformation R₉₀ o r_y=x  where the origin is the center of rotation?

• (-1, -4)
• (-4, -1)
• (1, 4)
• (4, 1)

Multiple Choice

The coordinates of triangle JRB  are ,J(1, -2) , R(-3, 6) and B(4, 5) .  What are the coordinates of the vertices of its image after the transformation T_{2, -1} o r_y-axis ?

• (3, 1), (-1, -7), (6, -6)
• (3, -3), (-1, 5), (6, 4)
• (1, -3), (5, 5), (-2, 4)
• (-1, -2), (3, 6), (-4, 5)

Multiple Choice

If the coordinates of point P are (2, -3) , then R₉₀ o R₁₈₀ is

• (-2, 3)
• (-2, -3)
• (3, -2)
• (-3, -2)

Multiple Choice

Name the series of transformations that maps ABC onto DEF

• reflect over x then translate left 6 up 1
• reflect over y then translate down 6 left 1
• translate right 6 down 1, then reflect over x
• rotate 90 clockwise then reflect over y