Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Question
**Reflection and Translation of Triangle PQR** Triangle \( PQR \) is reflected across the line \( y = 0 \). The image is then translated 5 units to the right, resulting in \( \triangle STU \). **Coordinate Plane Explanation:** - **Triangle \( PQR \):** - Vertex \( P \) is located at approximately (-5, 2). - Vertex \( Q \) is located at approximately (-3, 6). - Vertex \( R \) is located at approximately (-2, 3). - **Reflection Process:** - The vertices of triangle \( PQR \) are reflected over the x-axis (line \( y = 0 \)). - Reflected coordinates are: - \( P' \) at (-5, -2) - \( Q' \) at (-3, -6) - \( R' \) at (-2, -3) - **Translation Process:** - Each point of the reflected triangle is moved 5 units to the right. - Final coordinates are: - \( S \) at (0, -2) - \( T \) at (2, -6) - \( U \) at (3, -3) **Multiple Choice Statements:** A. \( PQ = ST \) B. \( PQ = TU \) C. \( m \angle R = m \angle U \) D. \( m \angle P = m \angle U \) Select all statements that apply after the reflection and translation processes have been completed. **Further Analysis:** - Make sure to check the lengths and angles of the subsequent triangle \( \triangle STU \) to verify the equality of sides or angles as per the given statements.
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Transcribed Image Text:**Reflection and Translation of Triangle PQR** Triangle \( PQR \) is reflected across the line \( y = 0 \). The image is then translated 5 units to the right, resulting in \( \triangle STU \). **Coordinate Plane Explanation:** - **Triangle \( PQR \):** - Vertex \( P \) is located at approximately (-5, 2). - Vertex \( Q \) is located at approximately (-3, 6). - Vertex \( R \) is located at approximately (-2, 3). - **Reflection Process:** - The vertices of triangle \( PQR \) are reflected over the x-axis (line \( y = 0 \)). - Reflected coordinates are: - \( P' \) at (-5, -2) - \( Q' \) at (-3, -6) - \( R' \) at (-2, -3) - **Translation Process:** - Each point of the reflected triangle is moved 5 units to the right. - Final coordinates are: - \( S \) at (0, -2) - \( T \) at (2, -6) - \( U \) at (3, -3) **Multiple Choice Statements:** A. \( PQ = ST \) B. \( PQ = TU \) C. \( m \angle R = m \angle U \) D. \( m \angle P = m \angle U \) Select all statements that apply after the reflection and translation processes have been completed. **Further Analysis:** - Make sure to check the lengths and angles of the subsequent triangle \( \triangle STU \) to verify the equality of sides or angles as per the given statements.
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