# 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

**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

**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 .

- AA clockwise rotation about
- BA clockwise rotation about
- CA counterclockwise rotation about
- DA counterclockwise rotation about
- EA translation one left and three up

Describe the single transformation that would map onto .

- AA clockwise rotation about
- BA clockwise rotation about
- CA rotation about
- 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
- Ba rotation of about
- Ca rotation of about
- 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: **

Does there exist a series of similarity transformations that would map quadrilateral to quadrilateral ? If yes, explain your answer.

- 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: **

The quadrilateral has been transformed onto quadrilateral which has then been transformed onto quadrilateral .

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

Hence, are quadrilaterals and similar?

- 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

**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

**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