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
Problem 1CT
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![### Graph the Image of Square JKLM After a 90° Counterclockwise Rotation Around the Origin
To create the new image of square JKLM after a 90-degree counterclockwise rotation around the origin, we need to apply the rotation transformation formula to each vertex of the square.
**Rotation Transformation Formula for 90° Counterclockwise (around the origin):**
For a point \((x, y)\), the new coordinates after a 90° counterclockwise rotation are given by:
\[ \text{New Coordinates} = (-y, x) \]
#### Steps:
1. **Identify the original coordinates of the vertices of square JKLM:**
- \( J (4, -5) \)
- \( K (6, -5) \)
- \( L (6, -7) \)
- \( M (4, -7) \)
2. **Apply the rotation transformation to each vertex:**
- For point \( J (4, -5) \):
\[ J' = (-(-5), 4) = (5, 4) \]
- For point \( K (6, -5) \):
\[ K' = (-(-5), 6) = (5, 6) \]
- For point \( L (6, -7) \):
\[ L' = (-(-7), 6) = (7, 6) \]
- For point \( M (4, -7) \):
\[ M' = (-(-7), 4) = (7, 4) \]
3. **Plot the new coordinates on the graph:**
- \( J' (5, 4) \)
- \( K' (5, 6) \)
- \( L' (7, 6) \)
- \( M' (7, 4) \)
4. **Connect the points to form the new square.**
Below is the image of the completed graph:
Helpful features:
- The graph has \(x\)- and \(y\)-axes ranging from \(-10\) to \(10\).
- The original square JKLM is located in the fourth quadrant.
- After the rotation, the new square \( J'K'L'M' \) will be located in the first quadrant.
### Final Square \( J'K](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F868053a9-8f29-4efd-8005-4438fb2086a0%2F6d2dc0ea-c270-48ca-a690-7553e53a953c%2Fy2m3jyf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graph the Image of Square JKLM After a 90° Counterclockwise Rotation Around the Origin
To create the new image of square JKLM after a 90-degree counterclockwise rotation around the origin, we need to apply the rotation transformation formula to each vertex of the square.
**Rotation Transformation Formula for 90° Counterclockwise (around the origin):**
For a point \((x, y)\), the new coordinates after a 90° counterclockwise rotation are given by:
\[ \text{New Coordinates} = (-y, x) \]
#### Steps:
1. **Identify the original coordinates of the vertices of square JKLM:**
- \( J (4, -5) \)
- \( K (6, -5) \)
- \( L (6, -7) \)
- \( M (4, -7) \)
2. **Apply the rotation transformation to each vertex:**
- For point \( J (4, -5) \):
\[ J' = (-(-5), 4) = (5, 4) \]
- For point \( K (6, -5) \):
\[ K' = (-(-5), 6) = (5, 6) \]
- For point \( L (6, -7) \):
\[ L' = (-(-7), 6) = (7, 6) \]
- For point \( M (4, -7) \):
\[ M' = (-(-7), 4) = (7, 4) \]
3. **Plot the new coordinates on the graph:**
- \( J' (5, 4) \)
- \( K' (5, 6) \)
- \( L' (7, 6) \)
- \( M' (7, 4) \)
4. **Connect the points to form the new square.**
Below is the image of the completed graph:
Helpful features:
- The graph has \(x\)- and \(y\)-axes ranging from \(-10\) to \(10\).
- The original square JKLM is located in the fourth quadrant.
- After the rotation, the new square \( J'K'L'M' \) will be located in the first quadrant.
### Final Square \( J'K
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