Understanding Transformations (Grade 10)

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Understanding Transformations

Square ABCD is translated horizontally and vertically. Its translated image is A'B'C'D'. What is true about the line segments [math]bar{A A'}[/math] and [math]bar{B B'} ?[/math] There may be more than one correct answer.
  1. They are parallel.
  2. They are perpendicular.
  3. They are equal in length.
  4. They bisect each other.
Quadrilateral ABCD is reflected over line [math]l[/math]. Its image is A'B'C'D'. What can be said about the relationship between line segment [math]bar(A A')[/math] and line [math] l ?[/math] Choose all correct answers.
  1. [math]l[/math] and [math]bar(A A')[/math] are perpendicular.
  2. [math]l[/math] and [math]bar(A A')[/math] are parallel.
  3. [math]l[/math] and [math]bar(A A')[/math] do not intersect.
  4. [math]l[/math] bisects [math]bar(A A')[/math].
Given quadrilateral ABCD, you rotate it [math]x[/math] degrees counterclockwise about the point [math]O[/math], resulting in the transformed image, A'B'C'D'. Which of the following are true? Choose all correct answers.
  1. [math]bar{A O} _|_ bar{A'O}[/math]
  2. [math]m ang AOA' = 180° - x°[/math]
  3. [math]bar(A O) ~= bar(A' O)[/math]
  4. [math]m ang AOA' = x°[/math]
The coordinates of triangle ABC's vertices are located at [math](2,3), (4,5),[/math] and [math](5,1)[/math], respectively. Triangle ABC is translated 5 units right and 3 units down, which we can call triangle A'B'C'. Of the three line segments formed by this translation, [math]bar{A A'}, bar{B B'},[/math] and [math]bar{C C'}[/math], which is the shortest?
  1. [math]bar{A A'}[/math]
  2. [math]bar{BB'}[/math]
  3. [math]bar{C C'}[/math]
  4. They are all the same length.
Given triangle ABC, whose vertices are [math](-3,0), (-1,6), (2,4)[/math], and circle [math](x-5)^2 + (y-4)^2 = 9[/math], which of the following points could be a vertex of the image of ABC if triangle ABC was rotated any number of degrees about the point [math](5,4)[/math]?
  1. [math](9, \ 4+i sqrt(7))[/math]
  2. [math](5,4)[/math]
  3. [math](3, \ 4+sqrt(5))[/math]
  4. [math](2,-4)[/math]
Triangle ABC is reflected over a line to produce its image, triangle A'B'C'. The vertices of triangle ABC are [math](1,1), (1,4), (4,1)[/math]. The vertices of its image are [math](6.6, 3.8), (4.2, 5.6), (4.8, 1.4)[/math]. What is the line over which triangle ABC was reflected?
  1. Cannot be determined.
  2. [math]y=1/2 x +1/2[/math]
  3. [math]y=-2x+7[/math]
  4. [math] y=-2x+10[/math]
Given one point of a polygon's pre-image, [math](3,2)[/math], its corresponding point on the transformed image, [math](8.6,-0.77)[/math], and the fact that the polygon is rotated counterclockwise about the point [math](5,-1)[/math], what is the angle of rotation?
  1. 120°
  2. 240°
  3. 37°
  4. 330°
The coordinates of point A of quadrilateral ABCD are (4, 7). If quadrilateral ABCD is rotated 60° counterclockwise, point A is transformed to, approximately, (0.0359, 5.87). If quadrilateral ABCD is rotated 150° clockwise, point A is transformed to, approximately, (4.13, -0.964). About what point are the rotations being performed?
  1. (1, 3)
  2. (3, 3)
  3. (2, 4)
  4. (3, 2)
Triangle ABC is translated 7 units right and 3 units up. The translated image is A'B'C' (not shown). Ellen believes that quadrilateral B'BCC' is a parallelogram and gives the following reasoning why. She knows that because rigid transformations do not change the size of a line segment, that [math]bar{B C} ~= bar{C' B'}[/math]. Also, [math]bar(B B') ~= bar{C C'}[/math] since line segments formed by corresponding points of translated images are congruent. James disagrees with her and says that she has not shown quadrilateral B'BCC' is a parallelogram. Who is correct and why?
Obtuse Triangle ABC v2
  1. Ellen is correct. Her statements are correct and sufficient to conclude that B'BCC' is a parallelogram.
  2. James is correct. Although Ellen's statements are correct, they are not sufficient to conclude that B'BCC' is a parallelogram.
  3. James is correct. Ellen's reasoning as to why [math]bar(B B') ~= bar{C C'}[/math] is not incorrect.
  4. James is correct. There are other ways to prove B'BCC' is a parallelogram.
Triangle ABC, whose coordinates are [math](-2,1), (1,3),[/math] and [math](3,2)[/math], is transformed to A'B'C', whose coordinates are [math](0.8,-7.4), (4.4, -7.2),[/math] and [math](5.4, -5.2)[/math]. Is this a rigid transformation, and if so, which transformation was performed? If it is a rigid transformation, assume that only one rotation, reflection, or translation (both vertical and horizontal) was performed.
  1. Not a rigid transformation
  2. Reflection
  3. Rotation
  4. Translation

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