Regents Exam Questions G.G.58: Compositions of Transformations 2
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Name: __________________________________
G.G.58: Compositions of Transformations: Define, investigate, justify, and apply
similarities (dilations and the composition of dilations and isometries)
1 If the coordinates of point A are
1)
2)
3)
4)
2 If the coordinates of P are
1)
2)
3)
4)
, what is the image of A under
, what are the coordinates of
3 Find the coordinates of the image of
4 If point A has coordinates
?
?
under the transformation
, what are the coordinates of
?
.
, the image of A under
Regents Exam Questions G.G.58: Compositions of Transformations 2
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5 The coordinates of the endpoints of
are
if it is reflected in the x-axis, then dilated by
and
. Is the image
as the image is if it is dilated by
the same
, then
reflected in the x-axis? Justify your answer. (The use of the accompanying grid is
optional.)
6 Triangle ABC has vertices
,
, and
. On the accompanying grid, draw
and label
. Graph and state the coordinates of
, the image of
after the
composition
.
Regents Exam Questions G.G.58: Compositions of Transformations 2
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7 Farmington, New York, has plans for a new triangular park. If plotted on a coordinate
grid, the vertices would be
,
, and
. However, a tract of land has
become available that would enable the planners to increase the size of the park, which is
based on the following transformation of the original triangular park,
. On the
grid below, graph and label both the original park
and its image, the new park
, following the transformation.
Regents Exam Questions G.G.58: Compositions of Transformations 2
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8 Given: F is the transformation
U is the transformation
N is the transformation
The coordinates of
are
,
, and
.
a. Sketch
and its image
after the transformation F.
b. Sketch
, the image of
after the transformation U.
c. Sketch
, the image of
after the transformation N.
d. Which transformation, F, U, or N, is a dilation?
Regents Exam Questions G.G.58: Compositions of Transformations 2
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9 a Triangle ABC has coordinates
,
, and
. On the graph below, draw
and label triangle ABC.
b Reflect the graph drawn in part a in the origin. State the coordinates of A', B', and C',
the images of A, B, and C.
c Dilate the graph drawn in part b using
. State the coordinates of A", B", C", the
images of A', B', and C'.
d Translate the graph drawn in part c using
C''', the images of A", B", and C".
. State the coordinates of A"', B''', and
Regents Exam Questions G.G.58: Compositions of Transformations 2
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Name: __________________________________
10 Triangle ABC has coordinates
,
a On the grid below, graph and label
b Graph and state the coordinates of
.
c Graph and state the coordinates of
d What is the ratio of the area of
, and
.
.
, the image of
after a half-turn
, the image of
to the area of
after
?
.
Regents Exam Questions G.G.58: Compositions of Transformations 2
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Name: __________________________________
11 On the graph below, sketch the triangle formed by points
,
, and
.
On the same set of axes, graph and state the coordinates of
a
, the image of
after the rotation
.
b
, the image of
after the translation
.
c
, the image of
after the dilation .
Is the composite transformation
an isometry? Explain your answer.
Regents Exam Questions G.G.58: Compositions of Transformations 2
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1 ANS: 4
After the dilation, the coordinates are (–6,9). After the reflection, the coordinates are (6,9).
REF: 010520b
2 ANS: 4
3 ANS:
REF: 019723siii
REF: 089340siii
4 ANS:
REF: 080010siii
5 ANS:
If
is reflected first, the coordinates of the endpoints of
are
. When the reflection is dilated, the coordinates of the endpoints of
are
. If
and
is dilated first, the coordinates of the endpoints of
dilation is reflected, the coordinates of the endpoints of
the same.
REF: 080028a
6 ANS:
REF: 068941siii
7 ANS:
are
are
and
and
and
. When the
. The images are
Regents Exam Questions G.G.58: Compositions of Transformations 2
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REF: 010930b
8 ANS:
N
REF: 068041siii
9 ANS:
;
;
REF: 069038siii
10 ANS:
;
;
REF: 089437siii
11 ANS:
;
preserved.
REF: 069938siii
;
; No, length is not