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

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, LET and L"E "T" are graphed in the coordinate plane where

LET ≅ L"E "T".

Which sequence of rigid motions maps LET onto L"E "T"?

1) a reflection over the y-axis followed by a reflection over the x-axis

2) a rotation of 180° about the origin3) a rotation of 90° counterclockwise about the

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

rotation of 90° clockwise about the origin

13 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


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

15 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".

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

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

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

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


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18 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.

19 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 .

20 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".

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

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


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22 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".

23 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 ″.


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24 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 ″.

25 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″?


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26 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 .

27 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

1) and 2) are wrong because the orientation of LET has changed, implying one reflection has occurred. The sequence in 4) moves LET back to Quadrant II.

REF: 062218geo 13 ANS: 3 REF: 011903geo 14 ANS:

T6,0 rx-axis

REF: 061625geo 15 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.

REF: 061730geo

ID: A

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19 ANS: R (−5,2),90° T−3,1 r x-axis


R180° about −12 , 1

2


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 24 ANS:

R180°

REF: 011635ge

ID: A

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25 ANS:

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

REF: 080327b 26 ANS:

A′(2,−1),B′(2,6),C ′(4,3); r y = x

REF: 019541siii 27 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

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

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