Which rule describes the transformation b

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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**Transformation Rules - Educational Resource**

**Question:**
Which rule describes the transformation between the given figures?

**Diagram:**
The provided diagram shows a coordinate plane with two figures. 

- The first figure, drawn in black, has vertices labeled \(E\), \(F\), \(I\), and \(R\).
- The second figure, drawn in blue, is a transformation of the black figure, with corresponding vertices labeled \(E'\), \(F'\), \(I'\), and \(R'\).

Both figures are connected by straight line segments forming the same shape, just in different orientations on the coordinate plane.

**Graph Details:**
- The \(x\)-axis is horizontal and the \(y\)-axis is vertical.
- Both axes are marked with equally spaced units.
- Both figures are polygons, and it is observable that the blue figure is a rotation of the black figure.

**Answer Choices:**
- ( ) rotation of 90 degrees counterclockwise
- ( ) rotation of 180 degrees
- ( ) reflection over the \(y\) axis
- ( ) reflection over the \(x\) axis
 
**Explanation:**
Analyze the orientation and position of the figures to determine the correct transformation rule.

- **Rotation of 90 degrees counterclockwise:** The figure would change positions in such a way that each vertex is turned 90 degrees in counterclockwise direction about the origin.
- **Rotation of 180 degrees:** The figure would be rotated 180 degrees around the origin.
- **Reflection over the \(y\) axis:** Each point of the figure on the right side of the \(y\) axis would appear mirrored on the left side.
- **Reflection over the \(x\) axis:** Each point of the figure above the \(x\) axis would appear mirrored below it.

**Transformation Identified:**
Careful observation of the figures suggests that the transformation rule is:

- ( ) rotation of 90 degrees counterclockwise
Transcribed Image Text:**Transformation Rules - Educational Resource** **Question:** Which rule describes the transformation between the given figures? **Diagram:** The provided diagram shows a coordinate plane with two figures. - The first figure, drawn in black, has vertices labeled \(E\), \(F\), \(I\), and \(R\). - The second figure, drawn in blue, is a transformation of the black figure, with corresponding vertices labeled \(E'\), \(F'\), \(I'\), and \(R'\). Both figures are connected by straight line segments forming the same shape, just in different orientations on the coordinate plane. **Graph Details:** - The \(x\)-axis is horizontal and the \(y\)-axis is vertical. - Both axes are marked with equally spaced units. - Both figures are polygons, and it is observable that the blue figure is a rotation of the black figure. **Answer Choices:** - ( ) rotation of 90 degrees counterclockwise - ( ) rotation of 180 degrees - ( ) reflection over the \(y\) axis - ( ) reflection over the \(x\) axis **Explanation:** Analyze the orientation and position of the figures to determine the correct transformation rule. - **Rotation of 90 degrees counterclockwise:** The figure would change positions in such a way that each vertex is turned 90 degrees in counterclockwise direction about the origin. - **Rotation of 180 degrees:** The figure would be rotated 180 degrees around the origin. - **Reflection over the \(y\) axis:** Each point of the figure on the right side of the \(y\) axis would appear mirrored on the left side. - **Reflection over the \(x\) axis:** Each point of the figure above the \(x\) axis would appear mirrored below it. **Transformation Identified:** Careful observation of the figures suggests that the transformation rule is: - ( ) rotation of 90 degrees counterclockwise
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