Comparing Rigid Transformations Quick Check

Question

1 of 51 of 5 Items
Question
Use the image to answer the question.

Beneath a cloudy sky, a large body of water is shown with mountains on either side and in the distance. Mirror images of the mountains can be seen in the water. Several trees line the water bank.
Source: Joe Dunckley/Shutterstock

This image could be used to help create a definition for which of the following?

(1 point)
Responses

reflection
reflection

dilation
dilation

rotation
rotation

translation

Which rigid transformation could be defined as a turn around a center point determined by an angle measured in degrees?(1 point)
Responses

a rotation
a rotation

a dilation
a dilation

a translation
a translation

a reflection

Which graph demonstrates a transformation that preserves both distance and angle measure?(1 point)
Responses

Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.
Image with alt text: Two squares, a smaller one inside a larger one, are plotted in quadrant 1 of a coordinate plane. The smaller square shares a vertex and two of its sides with parts of two sides of the larger square. The x- and y-axis both range from 0 to 8 in increments of 1.

Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.
Image with alt text: Two triangles of different sizes are plotted on a coordinate plane. The x-axis ranges from negative 4 to 8 in increments of 1, and the y-axis ranges from negative 4 to 10 in increments of 1.The larger triangle is plotted around the origin and extends into all four quadrants, and the smaller triangle extends between quadrants 1 and 2.

Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.
Image with alt text: Two equivalent triangles are plotted on a coordinate plane, one in quadrant 1 and one that starts in quadrant 2 and crosses into quadrant 1. The x-axis ranges from negative 4 to 7 in increments of 1, and the y-axis ranges from 0 to 7 in increments of 1. A line connects a vertex of the triangle in quadrant 2 to the matching vertex of the triangle in quadrant 1.

Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
Image with alt text: Two rectangles, a smaller one inside a larger one, are plotted around the origin on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 3 to 5 in increments of 1.
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△EFG is rotated −90 degrees (clockwise) to create △XYZ . Which of the following statements must be true?(1 point)
Responses

∠E≅∠X
angle upper E congruent to angle upper X

∠F≅∠Z
angle upper F congruent to angle upper Z

EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯
Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar

EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a(1 point)
Responses

reflection.
reflection.

translation.
translation.

dilation.
dilation.

rotation

Answer 1

Let's analyze each question and provide the correct responses based on the content.

1. This image could be used to help create a definition for which of the following?

   • Answer: reflection. (The mirror image of the mountains in the water represents a reflection.)

2. Which rigid transformation could be defined as a turn around a center point determined by an angle measured in degrees?

   • Answer: a rotation. (A rotation involves turning around a point.)

3. Which graph demonstrates a transformation that preserves both distance and angle measure?

   • Answer: (Based on the descriptions, the graphs that involve shapes like squares and equivalent triangles, which maintain size and angles, should be considered. The one with equivalent triangles or squares is likely correct.)
   • However, given that no specific graph image is visible, the general concept supports that equivalent figures (like squares and certain triangles) maintain angles and distances.

4. △EFG is rotated −90 degrees (clockwise) to create △XYZ. Which of the following statements must be true?

   • Answer: ∠E≅∠X (Angle E and angle X would be congruent after rotation.)

5. Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a

   • Answer: rotation. (Spinning around a central point represents a rotation.)

Feel free to provide any additional details or images, and I'll be glad to assist further!

Answer 2

are you sure these are correct

Answer 3

Let's double-check each response to ensure accuracy:

1. This image could be used to help create a definition for which of the following?

   • Correct Answer: Reflection. The description indicates a body of water showing mirror images of the mountains, which corresponds to the definition of a reflection.

2. Which rigid transformation could be defined as a turn around a center point determined by an angle measured in degrees?

   • Correct Answer: A rotation. This perfectly matches the definition of a rotation, where an object turns around a specified point.

3. Which graph demonstrates a transformation that preserves both distance and angle measure?

   • Based on the descriptions:
     • The graph with two equivalent triangles that are congruent maintains both distances and angles upon transformation.
   • Correct Answer: The one involving equivalent triangles or similar shapes would be accurate here, but without seeing the images, it's guided by the descriptions.

4. △EFG is rotated −90 degrees (clockwise) to create △XYZ. Which of the following statements must be true?

   • In this case, rotating a triangle does preserve angle measures and the relationship between corresponding angles:
     • Correct Answer: ∠E≅∠X (This is true: the angles retain congruency through the rotation).

5. Talia is playing with a plastic hoop that she spins around her waist. The spinning hoop resembles a

   • Correct Answer: Rotation. The act of spinning represents a form of rotation around a center point (her waist).

Based on this review, all initial answers provided are indeed correct. If there are specific concerns or if additional context (like images) is needed to clarify the third question further, please let me know!