Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 1
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Name: __________________________________
G.G.54: Compositions of Transformations: Define, investigate, justify, and apply
isometries in the plane (rotations, reflections, translations, glide reflections)
1 The accompanying graph represents the figure
Which graph represents
1)
2)
3)
4)
I.
I after a transformation defined by
?
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 2
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Name: __________________________________
2 Given point
. State the coordinates of the image of A under the composition
. [The use of the accompanying grid is optional.]
3 On the accompanying grid, graph and label
transformation
single transformation would map
, where A is
, A maps to
to
?
, and B maps to
and B is
. Under the
. Graph and label
. What
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 3
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Name: __________________________________
4 On the accompanying grid, graph and label
with vertices
,
, and
the same grid, graph and label
. the image of
after the transformation
.
5 The coordinates of the vertices of
are
,
, and
a On the graph below, draw and label
.
b Graph and state the coordinates of
, the image of
line
.
c Graph and state the coordinates of
, the image of
axis.
d Graph and state the coordinates of
, the image of
transformation
.
. On
.
after a reflection over the
after a reflection in the xafter the
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 4
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Name: __________________________________
6 Given:
with coordinates
,
a On the graph below, draw and label
b Graph and state the coordinates of
c Graph and state the coordinates of
axis.
d Graph and state the coordinates of
origin.
, and
.
.
, the image of
, the image of
, the image of
after the translation
.
after a reflection in the xafter a reflection in the
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 5
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Name: __________________________________
7 Triangle ABC has coordinates
,
a On the graph below, draw and label
b Graph and state the coordinates of
.
c Graph and state the coordinates of
.
d Graph and state the coordinates of
maps
onto
.
, and
.
.
, the image of
, the image of
, the image of
after a reflection in the line
following
after a translation that
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 6
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Name: __________________________________
8 Triangle ABC has coordinates
,
a On the grid below, draw and label
b Graph and state the coordinates of
.
c Write a transformation equivalent to
, and
.
.
, the image of
.
after the composition
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 7
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Name: __________________________________
9 On the graph below, draw and label
, whose vertices are
,
, and
the same set of axes, graph and state the coordinates of
a
, the image of
after
.
b
, the image of
after
.
c
, the image of
after
.
Based upon these graphs, write a single transformation that shows the composition
.
. On
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 8
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Name: __________________________________
10 Given
with points
,
, and
. On the grid below, sketch
. On the
same set of axes, graph and state the coordinates of
, the image of
after a
reflection in the line
. On the same set of axes, graph and state the coordinates of
,
the image of
after the translation
.
11 The coordinates of the vertices of parallelogram ABCD are
,
,
, and
State the coordinates of the vertices of parallelogram
that result from the
transformation
. [The use of the set of axes below is optional. ]
.
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 9
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Name: __________________________________
12 Given triangle ABC with coordinates
a On the graph below, draw and label
b Graph and label
, the image of
c Graph and label
d Graph and label
, the image of
, the image of
,
.
, and
after translation
.
.
after a reflection in the origin.
after a reflection in the line
.
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 10
www.jmap.org
Name: __________________________________
13 Triangle ABC has coordinates
,
a On the graph below, graph and label
b Graph and state the coordinates of
origin.
c Graph and state the coordinates of
.
d Graph and state the coordinates of
, and
.
, the image of
.
, the image of
, the image of
after a point reflection in the
reflected in the line
after translation
.
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 11
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Name: __________________________________
14 a On the accompanying grid, graph the equation
a.
b On the same grid, sketch the image of a under
in the interval
and label it
and label it b.
15 Graph and label the following equations, a and b, on the accompanying set of coordinate axes.
Describe the composition of transformations performed on a to get b.
Regents Exam Questions G.G.54: Compositions of Transformations 2
Page 12
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Name: __________________________________
16 A shape to be used in a computer game is placed on a Cartesian coordinate plane. The equation of
the shape is
. On the accompanying grid, graph the shape and label it a. In
the game, the shape is moved under the composition
. Draw this image, label it b, and
state its equation.
Regents Exam Questions G.G.54: Compositions of Transformations 2
www.jmap.org
1 ANS: 3
2 ANS:
PTS: 2
REF: 080219b
PTS: 2
3 ANS:
REF: 080626b
Single transformations include
PTS: 4
4 ANS:
REF: 080327b
PTS: 4
5 ANS:
REF: 060928b
;
PTS: 10
6 ANS:
;
REF: 088440siii
;
PTS: 10
7 ANS:
REF: 018739siii
;
PTS: 10
8 ANS:
;
REF: 018936siii
;
,
, and
.
Regents Exam Questions G.G.54: Compositions of Transformations 2
www.jmap.org
;
PTS: 4
9 ANS:
REF: 019541siii
;
PTS: 10
10 ANS:
;
REF: 089938siii
;
PTS: 5
11 ANS:
REF: 080141siii
PTS: 4
12 ANS:
REF: 060937ge
;
PTS: 10
13 ANS:
REF: 018541siii
;
PTS: 10
14 ANS:
PTS: 4
;
REF: 088741siii
REF: 010232b
;
;
Regents Exam Questions G.G.54: Compositions of Transformations 2
www.jmap.org
15 ANS:
,
PTS: 4
16 ANS:
REF: 080231b
PTS: 4
REF: 061029b
or