# Understanding Transformations (Grade 10)

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## Understanding Transformations

1.

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.

- They are parallel.
- They are perpendicular.
- They are equal in length.
- They bisect each other.

2.

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.

- [math]l[/math] and [math]bar(A A')[/math] are perpendicular.
- [math]l[/math] and [math]bar(A A')[/math] are parallel.
- [math]l[/math] and [math]bar(A A')[/math] do not intersect.
- [math]l[/math] bisects [math]bar(A A')[/math].

3.

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.

- [math]bar{A O} _|_ bar{A'O}[/math]
- [math]m ang AOA' = 180° - x°[/math]
- [math]bar(A O) ~= bar(A' O)[/math]
- [math]m ang AOA' = x°[/math]

4.

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?

- [math]bar{A A'}[/math]
- [math]bar{BB'}[/math]
- [math]bar{C C'}[/math]
- They are all the same length.

5.

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]?

- [math](9, \ 4+i sqrt(7))[/math]
- [math](5,4)[/math]
- [math](3, \ 4+sqrt(5))[/math]
- [math](2,-4)[/math]

6.

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?

- Cannot be determined.
- [math]y=1/2 x +1/2[/math]
- [math]y=-2x+7[/math]
- [math] y=-2x+10[/math]

7.

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?

- 120°
- 240°
- 37°
- 330°

8.

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, 3)
- (3, 3)
- (2, 4)
- (3, 2)

9.

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?

- Ellen is correct. Her statements are correct and sufficient to conclude that B'BCC' is a parallelogram.
- James is correct. Although Ellen's statements are correct, they are not sufficient to conclude that B'BCC' is a parallelogram.
- James is correct. Ellen's reasoning as to why [math]bar(B B') ~= bar{C C'}[/math] is not incorrect.
- James is correct. There are other ways to prove B'BCC' is a parallelogram.

10.

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.

- Not a rigid transformation
- Reflection
- Rotation
- Translation

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