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Regents Exam Questions Name: ________________________ G.CO.A.5: Compositions of Transformations 4www.jmap.org

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G.CO.A.5: Compositions of Transformations 4

1 Which transformation is equivalent to the composite line reflections r y − axis r y = x(AB)?1) a rotation2) a dilation3) a translation4) a glide reflection

2 Write a single translation that is equivalent to T3,−1 followed by T−5,5 .

3 Triangles ABC and RST are graphed on the set of axes below.

Which sequence of rigid motions will prove ABC ≅ RST?

1) a line reflection over y = x2) a rotation of 180° centered at (1,0)3) a line reflection over the x-axis followed by a

translation of 6 units right4) a line reflection over the x-axis followed by a

line reflection over y = 1

4 In the diagram below, A′B′C ′ is a transformation of ABC, and A″B″C ″ is a transformation of

A′B′C ′.

The composite transformation of ABC to A″B″C ″ is an example of a

1) reflection followed by a rotation2) reflection followed by a translation3) translation followed by a rotation4) translation followed by a reflection


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5 On the set of axes below, triangle ABC is graphed. Triangles A' B' C' and A"B"C", the images of triangle ABC, are graphed after a sequence of rigid motions.

Identify which sequence of rigid motions maps ABC onto A' B' C' and then maps A' B' C'

onto A"B"C".1) a rotation followed by another rotation2) a translation followed by a reflection3) a reflection followed by a translation4) a reflection followed by a rotation

6 On the set of axes below, pentagon ABCDE is congruent to A"B"C"D"E".

Which describes a sequence of rigid motions that maps ABCDE onto A"B"C"D"E"?1) a rotation of 90° counterclockwise about the

origin followed by a reflection over the x-axis2) a rotation of 90° counterclockwise about the

origin followed by a translation down 7 units3) a reflection over the y-axis followed by a

reflection over the x-axis4) a reflection over the x-axis followed by a

rotation of 90° counterclockwise about the origin


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7 In the diagram below, congruent figures 1, 2, and 3 are drawn.

Which sequence of transformations maps figure 1 onto figure 2 and then figure 2 onto figure 3?1) a reflection followed by a translation2) a rotation followed by a translation3) a translation followed by a reflection4) a translation followed by a rotation

8 A sequence of transformations maps rectangle ABCD onto rectangle A"B"C"D", as shown in the diagram below.

Which sequence of transformations maps ABCD onto A'B'C'D' and then maps A'B'C'D' onto A"B"C"D"?1) a reflection followed by a rotation2) a reflection followed by a translation3) a translation followed by a rotation4) a translation followed by a reflection


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9 Triangle ABC and triangle DEF are graphed on the set of axes below.

Which sequence of transformations maps triangle ABC onto triangle DEF?1) a reflection over the x-axis followed by a

reflection over the y-axis2) a 180° rotation about the origin followed by a

reflection over the line y = x3) a 90° clockwise rotation about the origin

followed by a reflection over the y-axis4) a translation 8 units to the right and 1 unit up

followed by a 90° counterclockwise rotation about the origin

10 Identify which sequence of transformations could map pentagon ABCDE onto pentagon A”B”C”D”E”, as shown below.

1) dilation followed by a rotation2) translation followed by a rotation3) line reflection followed by a translation4) line reflection followed by a line reflection

11 In the diagram below, ABC ≅ DEF.

Which sequence of transformations maps ABC onto DEF?1) a reflection over the x-axis followed by a

translation2) a reflection over the y-axis followed by a

translation3) a rotation of 180° about the origin followed by

a translation4) a counterclockwise rotation of 90° about the

origin followed by a translation


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12 On the set of axes below, ABC has vertices at A(−2,0), B(2,−4), C(4,2), and DEF has vertices at D(4,0), E(−4,8), F(−8,−4).

Which sequence of transformations will map ABC onto DEF?

1) a dilation of ABC by a scale factor of 2 centered at point A

2) a dilation of ABC by a scale factor of 12

centered at point A3) a dilation of ABC by a scale factor of 2

centered at the origin, followed by a rotation of 180° about the origin

4) a dilation of ABC by a scale factor of 12

centered at the origin, followed by a rotation of 180° about the origin

13 Describe a sequence of transformations that will map ABC onto DEF as shown below.

14 The graph below shows ABC and its image, A"B"C".

Describe a sequence of rigid motions which would map ABC onto A"B"C".


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15 On the set of axes below, ABC ≅ STU .

Describe a sequence of rigid motions that maps ABC onto STU .

16 On the set of axes below, ABC ≅ DEF.

Describe a sequence of rigid motions that maps ABC onto DEF.

17 Triangle ABC and triangle DEF are drawn below.

If AB ≅ DE , AC ≅ DF , and ∠A ≅ ∠D, write a sequence of transformations that maps triangle ABC onto triangle DEF.

18 On the set of axes below, ABC is graphed with coordinates A(−2,−1), B(3,−1), and C(−2,−4). Triangle QRS, the image of ABC, is graphed with coordinates Q(−5,2), R(−5,7), and S(−8,2).

Describe a sequence of transformations that would map ABC onto QRS .


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19 Quadrilateral MATH and its image M"A"T"H" are graphed on the set of axes below.

Describe a sequence of transformations that maps quadrilateral MATH onto quadrilateral M"A"T"H".

20 Quadrilaterals BIKE and GOLF are graphed on the set of axes below.

Describe a sequence of transformations that maps quadrilateral BIKE onto quadrilateral GOLF.

21 Trapezoids ABCD and A"B"C"D" are graphed on the set of axes below.

Describe a sequence of transformations that maps trapezoid ABCD onto trapezoid A"B"C"D".


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22 The graph below shows A' B' C ', the image of ABC after it was reflected over the y-axis. Graph

and label ABC, the pre-image of A' B' C '. Graph and label A″B″C ″, the image of A' B' C ' after it is reflected through the origin. State a single transformation that will map ABC onto

A″B″C ″.

23 The coordinates of ABC, shown on the graph below, are A(2,5), B(5,7), and C(4,1). Graph and label A' B′C ′, the image of ABC after it is reflected over the y-axis. Graph and label

A″B″C ″, the image of A′B′C ′ after it is reflected over the x-axis. State a single transformation that will map ABC onto

A″B″C ″.


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24 On the accompanying grid, graph and label AB, where A is (0,5) and B is (2,0). Under the transformation rx − axis r y − axis (AB), A maps to A″,

and B maps to B″. Graph and label A″B″. What single transformation would map AB to A″B″?

25 Triangle ABC has coordinates A(−1,2), B(6,2), and C(3,4).

a On the grid below, draw and label ABC. b Graph and state the coordinates of A′B′C ′,

the image of ABC after the composition R90° rx − axis .

c Write a transformation equivalent to R90° rx − axis .


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26 On the graph below, draw and label PQR, whose vertices are P(3,5), Q(9,5), and R(7,7). On the same set of axes, graph and state the coordinates ofa P ′Q ′R′, the image of PQR after R90° . b P″Q″R″, the image of P ′Q ′R′ after rx − axis .c P ″′Q″′R″′, the image of P″Q″R″ after

r y − axis .Based upon these graphs, write a single transformation that shows the composition r y − axis rx − axis R90° .

ID: A

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G.CO.A.5: Compositions of Transformations 4Answer Section

1 ANS: 1 REF: 018634siii 2 ANS:

T−2,4

REF: 019816siii 3 ANS: 2 REF: 081909geo 4 ANS: 4 REF: 061103ge 5 ANS: 4 REF: 061901geo 6 ANS: 2 REF: 012017geo 7 ANS: 4 REF: 061504geo 8 ANS: 1 REF: 081507geo 9 ANS: 1 REF: 011608geo 10 ANS: 3 REF: 011710geo 11 ANS: 2 REF: 061701geo 12 ANS: 3 REF: 011903geo 13 ANS:

T6,0 rx-axis

REF: 061625geo 14 ANS:

T0,−2 r y-axis


R90° or T2,−6 R (−4,2),90° or R270° r x-axis r y-axis


r y = 2 r y-axis


Rotate ABC clockwise about point C until DF AC. Translate ABC along CF so that C maps onto F.


R (−5,2),90° T−3,1 r x-axis

REF: 011928geo

ID: A

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19 ANS:

R180° about −12 ,

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Reflection across the y-axis, then translation up 5.


rotation 180º about the origin, translation 2 units down; rotation 180º about B, translation 6 units down and 6 units left; or reflection over x-axis, translation 2 units down, reflection over y-axis


rx-axis

REF: 061435ge 23 ANS:

R180°

REF: 011635ge

ID: A

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24 ANS:

Single transformations include R180° , R−180° , and r (0,0).

REF: 080327b 25 ANS:

A′(2,−1),B′(2,6),C ′(4,3); r y = x

REF: 019541siii 26 ANS:

P ′(−5,3),Q ′(−5,9),R′(−7,7); P ″(−5,−3),Q″(−5,−9),R″(−7,−7); P ″′(5,−3),Q″′(5,−9),R″′(7,−7); R270

REF: 089938siii

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