# Worksheet: Combining Transformations

In this worksheet, we will practice carrying out and describing combinations of transformations.

Q1:

The triangle has been transformed onto triangle which has then been transformed onto triangle . Describe the single transformation that maps onto .

• Aa rotation of clockwise about the point
• Ba dilation from the point by a scale factor of 2
• Ca dilation from the point by a scale factor of 3
• Da rotation of about the point
• Ea dilation from the point by a scale factor of 3

Describe the single transformation that maps onto .

• Aa rotation of clockwise about the point
• Ba rotation of about the point
• Ca rotation of about the point
• Da rotation of about the point
• Ea rotation of counterclockwise about the point

Hence, are triangles and similar?

• Ayes
• Bno

Q2:

A shape has been reflected in the line and then rotated clockwise about the origin to . Would and be congruent?

• Ayes
• Bno

Q3:

In the given figure, triangle has been transformed to triangle . Which of the following sequences of transformations could have been used? • Aa reflection in the line followed by a reflection in the -axis
• Ba rotation about the point followed by a translation three right
• Ca rotation about the point followed by a translation three right
• Da rotation about the origin followed by a translation three up
• Ea reflection in the -axis followed by a translation four right and four up

Q4:

In the given figure, triangle has been transformed to triangle by reflecting first in the and then reflecting in the . What single transformation would have mapped to ? • Aa rotation about the origin of
• Ba rotation about the origin of
• Ca rotation about the origin of
• Da reflection in the
• Ea reflection in the line

Q5:

is reflected in the -axis and then translated 5 units to the right. What is the image of point ? • A
• B
• C
• D
• E

Q6:

Starting with triangle , , and , apply the transformations: 1. reflect in the -axis, 2. reflect in the -axis, and 3. translate by 3 units right and 3 units up. What are the images of the vertices?

• A, ,
• B, ,
• C, ,
• D, ,
• E, ,

Q7:

The triangle has been transformed onto triangle which has then been transformed onto triangle then transformed onto as seen in the figure. Describe the single transformation that would map onto .

• EA translation one left and three up

Describe the single transformation that would map onto .

• DA reflection in the line
• EA translation two up

Describe the single transformation that would map onto .

• AA translation three right and two down
• BA translation two right and three down
• CA translation two left and three up
• DA translation three left and two up
• EA translation three left and two down

Hence, are triangles and congruent?

• AYes
• BNo

Q8:

The triangle has been transformed onto triangle which has then been transformed onto triangle . Describe the single transformation that maps onto .

• AA translation two up
• BA rotation counterclockwise about point
• CA rotation clockwise about point
• DA translation two down
• EA reflection in

Describe the single transformation that maps onto .

• AA dilation from the point by a scale factor of 2
• BA dilation from the point by a scale factor of
• CA translation two up
• DA dilation from the point by a scale factor of 2
• EA translation two down

Hence, are triangles and similar?

• AYes
• BNo

Q9:

The triangle has been transformed onto triangle that has then been transformed onto triangle . Describe the single transformation that maps onto .

• AA counterclockwise rotation about the origin
• BA clockwise rotation about the origin
• CA dilation from the origin by a scale factor of 2
• DA clockwise rotation about the origin
• EA dilation from point by a scale factor of 2

Describe the single transformation that maps onto .

• AA dilation from point by a scale factor of 2
• BA dilation from the origin by a scale factor of 2
• CA dilation from the origin by a scale factor of 3
• DA clockwise rotation about point
• EA clockwise rotation about point

Hence, are triangles and similar?

• AYes
• BNo

Q10:

The triangle has been transformed onto triangle which has then been transformed onto triangle . Describe the single transformation that maps onto .

• Aa translation two right and three up
• Ba translation three right and one up
• Ca reflection in the -axis
• Da translation three up and one right
• Ea reflection in the -axis

Describe the single transformation that maps onto .

• Aa translation one left and two up
• Ba dilation from the origin by a scale factor of 2
• Ca dilation from point by a scale factor of
• Da dilation from point by a scale factor of
• Ea translation one right and two up

Hence, are triangles and similar?

• Ayes
• Bno

Q11:

The triangle has been transformed onto triangle which has then been transformed onto triangle as seen in the figure. Describe the single transformation that would map to .

• Aa reflection in the line
• Da rotation of clockwise about point
• Ea rotation of clockwise about point

Describe the single transformation that would map to .

• Aa rotation of clockwise about point
• Ba rotation of counterclockwise about point
• Ca rotation of clockwise about point
• Da rotation of counterclockwise about point
• Ea translation two right

Hence, are triangles and congruent?

• Ayes
• Bno

Q12:

The triangles and in the figure are similar. Which of the following statements justifies this? • ATriangle can be mapped onto triangle by a sequence of transformations: first, a reflection in the , and then a dilation of the image by a scale factor of three from point .
• BTriangle can be mapped onto triangle by a sequence of transformations: first, a dilation by a scale factor of three from point , and then a translation of the image two down.
• CTriangle can be mapped onto triangle by a sequence of transformations: first, a dilation by a scale factor of three from point , and then a translation of the image eight down.
• DTriangle can be mapped onto triangle by a sequence of transformations: first, a dilation by a scale factor of three from point , and then a reflection of the image in the .
• ETriangle can be mapped onto triangle by a sequence of transformations: first, a reflection in the , and then a translation of the image four right.

Q13: • AThere is no series of similarity transformations.
• BYes, quadrilateral could be dilated by a scale factor of 3, rotated, and then reflected to quadrilateral .
• CYes, quadrilateral could be dilated by a scale factor of 2 and then rotated to quadrilateral .
• DYes, quadrilateral could be dilated by a scale factor of 3 and then reflected to quadrilateral .
• EYes, quadrilateral could be dilated by a scale factor of 2, rotated, and then reflected to quadrilateral .

Q14:

The triangle with vertices , , and was transformed to , , and and then to , , and . Which of the following describes these transformations?

• AIt was translated 2 units right and 5 units down, and then it was rotated counterclockwise about the point .
• BIt was rotated counterclockwise about the point , and then it was translated 2 units right and 5 units down.
• CIt was translated 2 units left and 5 units up, and then it was rotated clockwise about the point .
• DIt was translated 2 units left and 5 units up, and then it was rotated clockwise about the point .

Q15:

The triangle has been transformed onto triangle which has then been transformed onto triangle as seen in the figure. Describe the single transformation that would map onto .

• AA counterclockwise rotation of about point
• BA clockwise rotation of about point
• CA rotation of about point
• DA translation four left
• EA translation two right and eight down

Describe the single transformation that would map onto .

• AA translation two right and eight down
• BA translation two left and eight up
• CA translation eight right and two down
• DA translation two left and eight down
• EA translation two right and eight up

Hence, are triangles and congruent?

• ANo
• BYes

Q16: Describe the single transformation that maps onto .

• Aa reflection in the -axis
• Ba dilation from the point by a scale factor of 3
• Ca translation two right
• Da reflection in the -axis
• Ea translation two left

Describe the single transformation that maps onto .

• Aa reflection in the -axis
• Ba dilation from the point by a scale factor of
• Ca dilation from the point by a scale factor of 3
• Da dilation from the point by a scale factor of 3
• Ea reflection in the -axis

• Ano
• Byes

Q17:

Triangle has been transformed onto triangle which has then been transformed onto triangle . Describe the single transformation that maps onto .

• AA dilation from point by a scale factor of 3
• BA dilation from the point by a scale factor of 3
• CA translation two right and two up
• DA translation two left and two down
• EA dilation from point by a scale factor of 2

Describe the single transformation that maps onto .

• AA translation six right
• BA counterclockwise rotation about point
• CA counterclockwise rotation about point
• DA translation six left
• EA rotation counterclockwise about point

Hence, are triangles and similar?

• ANo
• BYes

Q18:

Find the image of point after applying the translation followed by a rotation counterclockwise about the origin.

• A
• B
• C
• D
• E

Q19:

Reflect Triangle in the -axis and then in the -axis. Which triangle is its image? • A
• B
• C
• D

Q20:

Reflect Triangle in the -axis and then in the -axis. Which triangle is its image? • A
• B
• C
• D

Q21:

In the given figure, what combination of transformations would map circle onto circle ? • Aa translation of four left and six down, followed by a dilation of scale factor
• Ba translation of six left and four down, followed by a dilation of scale factor
• Ca translation of four left and six down, followed by a dilation of scale factor
• Da translation of six right and four up, followed by a dilation of scale factor
• Ea translation of four left and six up, followed by a dilation of scale factor

Q22:

Does there exist a series of similarity transformations that would map triangle to triangle ? If yes, explain your answer. • ANo series of similarities exists because the two triangles are of different sizes.
• BYes, triangle could be dilated by a scale factor of 3, rotated, and then reflected.
• CYes, triangle could be dilated by a scale factor of 3 and then reflected.
• DYes, triangle could be dilated by a scale factor of 2 and then reflected.
• EYes, triangle could be dilated by a scale factor of 2 and then rotated.

Q23:

In the given figure, what combination of transformations would map circle onto circle ? • Aa translation of two right and six down followed by a dilation of scale factor two
• Ba translation of two left and six up followed by a dilation of scale factor two
• Ca translation of four left and two down followed by a dilation of scale factor one
• Da translation of six left and two up followed by a dilation of scale factor one
• Ea translation of six right and two down followed by a dilation of scale factor two

Q24:

First, translate the given triangle two right and two down, and then rotate this image about the origin. Which of the following sets of coordinates will be the vertices of the image? • A, and
• B, and
• C, and
• D, and
• E, and

Q25:

The triangle has been transformed to triangle which has then been transformed to triangle . Describe the single transformation that maps to .

• Aa dilation from the origin by a scale factor of 2
• Ba dilation from the origin by a scale factor of 3
• Ca reflection in the -axis
• Da dilation from point by a scale factor of 3
• Ea reflection in the -axis

Describe the single transformation that maps to .

• Aa dilation from the origin by a scale factor of 3
• Ba reflection in the -axis
• Ca dilation from the origin by a scale factor of
• Da dilation from the origin by a scale factor of 2
• Ea reflection in the -axis

Hence, are triangles and similar?

• Ayes
• Bno