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This image could be used to help create a definition for which of the following? (1 point) Responses dilation dilation rotation rotation translation translation reflection

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To help provide an appropriate answer, I would need to know what the image depicts. However, based on the list of geometric transformations you provided, I can give brief definitions for each:

  1. Dilation: A transformation that alters the size of a shape but keeps its proportion and center point the same.

  2. Rotation: A transformation that turns a shape around a fixed point at a certain angle.

  3. Translation: A transformation that slides a shape in any direction without altering its size, shape, or orientation.

  4. Reflection: A transformation that flips a shape over a line, creating a mirror image.

If you describe the image or its features, I can help indicate which geometric transformation it relates to!

Use the image to answer the question. Source: Joe Dunckley/Shutterstock This image could be used to help create a definition for which of the following? (1 point) Responses dilation dilation rotation rotation translation translation reflection reflection

Based on the options provided and the typical use of such images in geometry, if the image shows a shape being resized (but not flipped or moved in another direction), it would likely relate to dilation. If it shows a shape being flipped over a line, it would relate to reflection. If it shows a shape being turned around a point, it relates to rotation. Lastly, if it shows a shape simply being moved from one location to another without changing its size or orientation, it relates to translation.

Without the image itself, I recommend considering what transformation is being illustrated to determine the best answer from the provided choices. If you can describe what's happening in the image, I'd be happy to help further!

△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 EF¯¯¯¯¯¯¯¯≅XZ¯¯¯¯¯¯¯¯ Modifying above upper E upper F with bar congruent to Modifying above upper X upper Z with bar ∠F≅∠Z angle upper F congruent to angle upper Z EG¯¯¯¯¯¯¯¯≅XY¯¯¯¯¯¯¯¯

Given that triangle \( \triangle EFG \) is rotated \( -90 \) degrees (clockwise) to form triangle \( \triangle XYZ \), we know that the corresponding vertices of the triangles will match up in a specific way due to the nature of rotations.

In general, when a figure is rotated, the following properties hold true:

  1. Corresponding angles of the original figure and the rotated figure are congruent.
  2. Corresponding sides of the original figure and the rotated figure are also congruent.

Based on this information, we can assess the statements provided:

  1. \( \angle E \cong \angle X \): Since after a \( -90^\circ \) rotation, \( \angle E \) (from vertex E) will correspond to \( \angle X \) (in the new triangle), this statement is true.

  2. \( EF \cong XZ \): This states that the side connecting vertices E and F is congruent to the side connecting vertices X and Z. Since they are corresponding sides after the rotation, this statement is true.

  3. \( \angle F \cong \angle Z \): Following the same reasoning, as \( \angle F \) corresponds to \( \angle Z \) after rotation, this statement is also true.

  4. \( EG \cong XY \): As the side EF corresponds to XZ and side EG corresponds to side XY (due to the nature of the rotation), this statement is similarly true.

Thus, all statements—1, 2, 3, and 4—are true based on the properties of rotation. However, if you are asked to select only one statement that must be true, it might depend on the specific context or focus of your question.

If you only need to choose one:

  • Answer: \( \angle E \cong \angle X \) (if focusing solely on angles), or \( EF \cong XZ \) (if focusing on sides).

If you're asked for a specific option that must be true among the provided options, you could choose either depending on what aspect (angles or sides) is more central to your question.

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

Talia spinning a plastic hoop around her waist resembles a rotation.

In this case, the hoop moves around a central point (her waist), similar to how a shape rotates around a point in geometry. Therefore, the most appropriate response is rotation.