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This printable supports Common Core Mathematics Standard HSG-SRT.A.2

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# Similarity Transformations (Grade 10)

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## Similarity Transformations

1.
$Delta ABC$ is rotated 90° about the origin, reflected over the y-axis, and then dilated by a factor of 3, with the center of dilation being the origin. Therefore, $Delta A'B'C' \ ~ \ Delta ABC$, such that $(AB)/(A'B') != 1$.
1. True
2. False
2.
$Delta FGH$ is translated 4 units right and 3 units up, rotated 45° about the point (4,5), and then reflected over the line $y = 3x-7$. The image $Delta F'G'H'$ is similar to the pre-image, such that $(FG)/(F'G') != 1$.
1. True
2. False
3.
$Delta HJK$ is rotated 275° about the origin and then translated 3 units left and 3 units up, resulting in the image $Delta H'J'K'$. This new triangle is then dilated by a factor of $3/4$, with the center of dilation being the point $H'$. $Delta H^**J^**K^**$ represents the triangle after the dilation. Therefore, $Delta HJK \ ~ \ Delta H^**J^**K^**$, such that $(HJ)/(H^**J^**) !=1$.
1. True
2. False
4.
Quadrilateral $WXYZ$ is translated 9 units to the right, reflected over the line $y=x$, and then dilated by a factor of -2, with the center of dilation being (-2,-2). The image, quadrilateral $W'X'Y'Z'$ is similar to the pre-image $WXYZ$, such that $(W'X')/(WX) != 1$.
1. True
2. False
5.
Quadrilateral ABCD is translated 3 units left and 2 units up. It is then rotated 180° about the origin. Then vertices A and B only are dilated by a factor of 2, with point C being the center of dilation. The image, quadrilateral A'B'C'D', and its pre-image are similar, such that $(A'B')/(AB) != 1$.
1. True
2. False
6.
The coordinates of the vertices of $Delta ABC$ are A(3,2), B(4,5), and C(1,1). The coordinates of the vertices of $Delta LMN$ are L(8,-2), M(10,4), and N(4,-4). Which of the following sequences of transformations, applied to $Delta ABC$, shows that $Delta ABC \ ~ \ Delta LMN ?$
1. A translation of 2 units right and 2 units down, and then a dilation of factor $3/2$ centered at the origin.
2. A translation of 2 units right, a reflection over the x-axis, and then a dilation of factor 3 centered at the origin.
3. A translation of 1 unit right and 3 units down, and then a dilation of factor 2 centered at the origin.
4. A translation of 3 units left and 1 unit up, and then a dilation of factor -2 centered at the origin.
7.
The coordinates of the vertices of $Delta FGH$ are $F(0,1)$, $G(3,-1)$, and $H(5,3)$. The coordinates of the vertices of $Delta SRT$ are $S(0,-1)$, $R(3/2,0)$, and $T(5/2, -2)$. Which of the following sequences of transformations, applied to $Delta FGH$, shows that $Delta FGH \ ~ \ Delta SRT ?$
1. A translation 2 units down, and then a dilation by a factor of $1/2$ centered at the origin.
2. A rotation of 180° about the origin, and then a dilation by a factor of $1/2$ centered at the origin.
3. A translation of a $1/2$ unit up, and then a dilation by a factor of $1/2$ centered at the origin.
4. A translation of 1 unit up, a reflection over the x-axis, and then a dilation by a factor of $1/2$ centered at the origin.
8.
The coordinates of the vertices of $Delta CDE$ are C(-4,-4), D(-1,-1), and E(0,5). The coordinates of the vertices of $Delta JKL$ are J(-8,8), K(-2,2), and L(10,0). Which of the following sequence of transformations, applied to $Delta CDE$, shows that $Delta CDE \ ~ \ Delta JKL ?$
1. A rotation of 90° counterclockwise about the origin, and then a dilation of factor -2 centered at the origin.
2. A reflection over the line $y=2$, and then a dilation of factor 2 centered at the origin.
3. A translation of 2 units left and 4 units up, and then a dilation of factor 2 centered at the origin.
4. A reflection over the line $y=x$, and then a dilation of factor $-2$ centered at the origin.
9.
$Delta EFG$ has vertices located at E(3,7), F(-1,4), and G(2,1). $Delta TUV$ has vertices located at T(-9,15), U(-1,9), and V(-7,3). Which of the following sequences of transformations, applied to $Delta EFG$, shows that $Delta EFG \ ~ \ Delta TUV ?$
1. A translation of 1 unit right and 1 unit up, a rotation of 90° counterclockwise about the origin, and then a dilation of factor 2 centered at the origin.
2. A translation of 6 units right and 4 units down, a rotation of 90° about the origin, and then a dilation of factor 2 centered at (3,3).
3. A translation of 1 unit right and 1 unit up, a reflection over the y-axis, and then a dilation of factor 2 centered at (1,1).
4. A translation of 3 units left and 4 units up, and then a dilation of factor $3/2$ centered at the origin.
10.
The coordinates of the vertices of $Delta ABC$ are $A(-9,7)$, $B(-5,6)$, and $C(-7,2)$. The coordinates of the vertices of $Delta DEF$ are $D(1/2,17/2)$, $E(5/2, 8)$, and $F(3/2,6)$. Which of the following sequences of transformations, applied to $Delta ABC$, shows that $Delta ABC \ ~ \ Delta DEF ?$
1. A translation of 5 units left and 7 units down, a rotation of 270° counterclockwise about the origin, and then a dilation of factor $1/2$ centered at (1,3).
2. A translation of 1 unit right and 2 units down, a rotation of 180° counterclockwise about the origin, and then a dilation of factor $-1/2$ centered at (3,4).
3. A translation of 8 units right, a reflection over the y-axis, and then a dilation of factor $3/2$ centered at the origin.
4. A translation of 3 units right and 1 unit up, a rotation of 90° counterclockwise about the origin, and then a dilation of factor $1/2$ centered at (1,1).
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