Similarity Transformations (Grade 10)

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Similarity Transformations

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

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