G.SRT.A.2.CompositionsofTransformations2.doc
1 In the diagram below, [pic] is the image of [pic] after a clockwise rotation of 180° and a dilation where [pic], [pic], [pic], [pic], [pic], and [pic].
[pic]
Which relationship must always be true?
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
2 In the diagram below, [pic] is the image of [pic] after a reflection over the line AC followed by a dilation of scale factor [pic] centered at point A.
[pic]
Which statement must be true?
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
3 Given: [pic], [pic], and [pic]
[pic]
What is a correct sequence of similarity transformations that shows [pic]?
|1) |a rotation of 180 degrees about point E followed by a horizontal |
| |translation |
|2) |a counterclockwise rotation of 90 degrees about point E followed |
| |by a horizontal translation |
|3) |a rotation of 180 degrees about point E followed by a dilation |
| |with a scale factor of 2 centered at point E |
|4) |a counterclockwise rotation of 90 degrees about point E followed |
| |by a dilation with a scale factor of 2 centered at point E |
4 Which sequence of transformations will map [pic] onto [pic]?
[pic]
|1) |reflection and translation |
|2) |rotation and reflection |
|3) |translation and dilation |
|4) |dilation and rotation |
5 After a composition of transformations, the coordinates [pic], [pic], and [pic] become [pic], [pic], and [pic], as shown on the set of axes below.
[pic]
Which composition of transformations was used?
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
6 Triangle PQR is shown on the set of axes below.
[pic]
Which quadrant will contain point R", the image of point R, after a 90° clockwise rotation centered at [pic] followed by a reflection over the x-axis?
|1) |I |
|2) |II |
|3) |III |
|4) |IV |
7 In regular hexagon ABCDEF shown below, [pic], [pic], and [pic] all intersect at G.
[pic]
When [pic] is reflected over [pic] and then rotated 180° about point G, [pic] is mapped onto
|1) |[pic] |
|2) |[pic] |
|3) |[pic] |
|4) |[pic] |
8 In the diagram below, triangles XYZ and UVZ are drawn such that [pic] and [pic].
[pic]
Describe a sequence of similarity transformations that shows [pic] is similar to [pic].
9 As shown on the set of axes below, [pic] has vertices [pic], [pic], and [pic]. Graph and state the coordinates of [pic], the image of [pic] after the transformation [pic].
[pic]
10 Triangle ABC has vertices [pic], [pic] and [pic]. State and label the coordinates of the vertices of [pic], the image of [pic], following the composite transformation [pic]. [The use of the set of axes below is optional.]
[pic]
11 The coordinates of the vertices of parallelogram SWAN are [pic], [pic], [pic], and [pic]. State and label the coordinates of parallelogram [pic], the image of SWAN after the transformation [pic]. [The use of the set of axes below is optional.]
[pic]
12 Triangle ABC has coordinates [pic], [pic], and [pic].
a On the grid below, graph and label [pic].
b Graph and state the coordinates of [pic], the image of [pic] after a half-turn [pic].
c Graph and state the coordinates of [pic], the image of [pic] after [pic].
d What is the ratio of the area of [pic] to the area of [pic]?
[pic]
13 The coordinates of the vertices of [pic] [pic], [pic] and [pic]. On the grid below, graph and label [pic], the result of the composite transformation [pic]. State the coordinates of [pic], [pic], and [pic].
[pic]
14 The coordinates of the endpoints of [pic] are [pic] and [pic]. Is the image [pic] the same if it is reflected in the x-axis, then dilated by [pic]as the image is if it is dilated by [pic], then reflected in the x-axis? Justify your answer. (The use of the accompanying grid is optional.)
[pic]
15 Triangle ABC has vertices [pic], [pic], and [pic]. On the accompanying grid, draw and label [pic]. Graph and state the coordinates of [pic], the image of [pic] after the composition [pic].
[pic]
16 Farmington, New York, has plans for a new triangular park. If plotted on a coordinate grid, the vertices would be [pic], [pic], and [pic]. 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, [pic]. On the grid below, graph and label both the original park [pic] and its image, the new park [pic], following the transformation.
[pic]
17 a Triangle ABC has coordinates [pic], [pic], and [pic]. 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 [pic]. State the coordinates of A", B", C", the images of A', B', and C'.
d Translate the graph drawn in part c using [pic]. State the coordinates of A"', B''', and C''', the images of A", B", and C".
[pic]
18 On the graph below, sketch the triangle formed by points [pic], [pic], and [pic]. On the same set of axes, graph and state the coordinates of
a [pic], the image of [pic] after the rotation [pic].
b [pic], the image of [pic] after the translation [pic].
c [pic], the image of [pic] after the dilation [pic].
Is the composite transformation [pic] an isometry? Explain your answer.
[pic]
1 ANS: 4 REF: 081514geo
2 ANS: 2 REF: 011702geo
3 ANS: 4 REF: 081609geo
4 ANS: 4 REF: 061608geo
5 ANS: 3 REF: 060908ge
6 ANS: 1 REF: 012022geo
7 ANS: 1 REF: 081804geo
8 ANS:
Triangle [pic] is the image of [pic] after a rotation about point Z such that [pic] coincides with [pic]. Since rotations preserve angle measure, [pic] coincides with [pic], and corresponding angles X and Y, after the rotation, remain congruent, so [pic]. Then, dilate [pic] by a scale factor of [pic] with its center at point Z. Since dilations preserve parallelism, [pic] maps onto [pic]. Therefore, [pic].
REF: spr1406geo
9 ANS:
[pic] [pic]
REF: 081136ge
10 ANS:
[pic] [pic]
REF: 011336ge
11 ANS:
[pic] [pic], [pic], [pic], and [pic]
REF: 061335ge
12 ANS:
[pic]; [pic]; [pic]
REF: 089437siii
13 ANS:
[pic] [pic]
REF: 081036ge
14 ANS:
[pic] If [pic] is reflected first, the coordinates of the endpoints of [pic] are [pic] and [pic]. When the reflection is dilated, the coordinates of the endpoints of [pic] are [pic] and [pic]. If [pic] is dilated first, the coordinates of the endpoints of [pic] are [pic] and [pic]. When the dilation is reflected, the coordinates of the endpoints of [pic] are [pic] and [pic]. The images are the same.
REF: 080028a
15 ANS:
[pic]
REF: 068941siii
16 ANS:
[pic]
REF: 010930b
17 ANS:
[pic]; [pic]; [pic]
REF: 069038siii
18 ANS: [pic]; [pic]; [pic]; No, length is not preserved.
REF: 069938siii
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