# Worksheet: Combining Transformations

Q1:

is reflected in the -axis and then translated 5 units to the right. What is the image of point ?

• A
• B
• C
• D
• E

Q2:

is reflected in the -axis and then translated 2 units to the right. What is the image of point ?

• A
• B
• C
• D
• E

Q3:

The triangles and in the figure are similar. Which of the following statements justifies this?

• A Triangle 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.
• B Triangle can be mapped onto triangle by a sequence of transformations: first, a reflection in the , and then a translation of the image four right.
• C Triangle 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 .
• D Triangle 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 .
• E Triangle 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.

Q4:

A transformation maps point to point . We say that is the of .

• Apostimage
• Bpreimage
• Cimage

Q5:

A transformation maps point to point . We say that is the of .

• Apostimage
• Bimage
• Corigin
• Dpreimage
• Efigure

Q6:

• A Yes, quadrilateral could be dilated by a scale factor of 2 and then rotated to quadrilateral .
• B Yes, quadrilateral could be dilated by a scale factor of 3, rotated, and then reflected to quadrilateral .
• C Yes, quadrilateral could be dilated by a scale factor of 3 and then reflected to quadrilateral .
• D Yes, quadrilateral could be dilated by a scale factor of 2, rotated, and then reflected to quadrilateral .
• EThere is no series of similarity transformations.

Q7:

Triangle can be reflected and then translated onto .

Determine the length of .

Determine the measure of angle .

Q8:

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

Q9:

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

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

Q10:

Describe the single transformation that maps onto .

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

Describe the single transformation that maps onto .

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

• Ano
• Byes

Q11:

In the given figure, triangle has been transformed to triangle by reflecting first in the -axis and then reflecting in the axis. What single transformation would have mapped to ?

• A a rotation about the origin of
• B a reflection in the line
• C a reflection in the -axis
• D a rotation about the origin of
• Ea rotation about the origin of

Q12:

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

Describe the single transformation that maps onto .

• Aa dilation from the point by a scale factor of 3
• Ba dilation from the point by a scale factor of 2
• Ca translation two left and two down
• Da dilation from the point by a scale factor of 3
• Ea translation two right and two up

Describe the single transformation that maps onto .

• Aa rotation counterclockwise about the point
• Ba translation six left
• Ca counterclockwise rotation about the point
• Da counterclockwise rotation about the point
• Ea translation six right

Hence, are triangles and similar?

• Ano
• Byes

Q13:

Find the image of point after translation by followed by a rotation about the origin through an angle of .

• A
• B
• C
• D
• E

Q14:

Find the image of point after translation by followed by a rotation about the origin through an angle of .

• A
• B
• C
• D
• E

Q15:

Find the image of point after translation by followed by a rotation about the origin through an angle of .

• A
• B
• C
• D
• E

Q16:

Reflect Triangle in the -axis and then in the -axis. Which triangle is its image?

• A
• B
• C
• D

Q17:

Reflect Triangle in the -axis and then in the -axis. Which triangle is its image?

• A
• B
• C
• D

Q18:

Which of the following statements will be true for two triangles that are similar.

• AOne triangle can sometimes (but not always) be mapped to the other by a translation, reflection, rotation, dilation, or a combination of these transformations.
• BOne triangle can always be mapped to the other by a translation, reflection, rotation, or a combination of these transformations.
• COne triangle can always be mapped to the other by a translation, reflection, rotation, dilation, or a combination of these transformations.

Q19:

In the given figure, what combination of transformations would map circle onto circle ?

• Aa translation of six right and four up, followed by a dilation of scale factor
• Ba translation of four left and six 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 left and four down, followed by a dilation of scale factor
• Ea translation of four left and six up, followed by a dilation of scale factor

Q20:

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

• A Yes, triangle could be dilated by a scale factor of 3 and then reflected.
• B Yes, triangle could be dilated by a scale factor of 2 and then reflected.
• C Yes, triangle could be dilated by a scale factor of 2 and then rotated.
• D Yes, triangle could be dilated by a scale factor of 3, rotated, and then reflected.
• E No series of similarities exists because the two triangles are of different sizes.

Q21:

In the given figure, what combination of transformations would map circle onto circle ?

• A a translation of six left and two up followed by a dilation of scale factor one
• B a translation of two right and six down followed by a dilation of scale factor two
• C a translation of two left and six up followed by a dilation of scale factor two
• D a translation of six right and two down followed by a dilation of scale factor two
• E a translation of four left and two down followed by a dilation of scale factor one