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`y 4 P. -6 -4 -2 2 T. A PO = ST

`y 4 P. -6 -4 -2 2 T. A PO = ST

Elementary Geometry For College Students, 7e
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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**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.
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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