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In Exercises 17 and 19, graph A RST with vertices R(4, 1), S(7,3), and T(6,4) and its image after the glide reflection. 17) Translation: (x,y) → (x, y - 1) - Reflection: in the y-axis 19) Translation: (x,y) → (x, y + 4) Reflection: in the line x = 3

In Exercises 17 and 19, graph A RST with vertices R(4, 1), S(7,3), and T(6,4) and its image after the glide reflection. 17) Translation: (x,y) → (x, y - 1) - Reflection: in the y-axis 19) Translation: (x,y) → (x, y + 4) Reflection: in the line x = 3

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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In Exercises 17 and 19, graph triangle \( \triangle RST \) with vertices \( R(4, 1) \), \( S(7, 3) \), and \( T(6, 4) \) and its image after the glide reflection. **Exercise 17:** - **Translation:** \( (x, y) \rightarrow (x, y - 1) \) - **Reflection:** in the \( y \)-axis **Exercise 19:** - **Translation:** \( (x, y) \rightarrow (x, y + 4) \) - **Reflection:** in the line \( x = 3 \) The graph grid accompanying this text shows arrows indicating vertical movement consistent with the translations described (e.g., up or down for \(\Delta y\)). The grid is marked at intervals, with "8" indicating a certain point on the axes, although the specific graph of triangle \( \triangle RST \) and its image after these transformations is not explicitly drawn in this portion of the image.
Transcribed Image Text:In Exercises 17 and 19, graph triangle \( \triangle RST \) with vertices \( R(4, 1) \), \( S(7, 3) \), and \( T(6, 4) \) and its image after the glide reflection. **Exercise 17:** - **Translation:** \( (x, y) \rightarrow (x, y - 1) \) - **Reflection:** in the \( y \)-axis **Exercise 19:** - **Translation:** \( (x, y) \rightarrow (x, y + 4) \) - **Reflection:** in the line \( x = 3 \) The graph grid accompanying this text shows arrows indicating vertical movement consistent with the translations described (e.g., up or down for \(\Delta y\)). The grid is marked at intervals, with "8" indicating a certain point on the axes, although the specific graph of triangle \( \triangle RST \) and its image after these transformations is not explicitly drawn in this portion of the image.
**Translation and Reflection in Mathematics** **Translation:** In this exercise, point 17 describes a translation on the coordinate plane. The translation is defined by the transformation: \[ (x, y) \rightarrow (x, y - 1) \] This means that every point on the plane is moved one unit downward, parallel to the y-axis. The x-coordinate remains unchanged, while the y-coordinate is decreased by 1. **Reflection:** Reflection in this context refers to flipping a figure over a specific line. Here, the reflection is in the y-axis. This operation takes each point on the plane and maps it to a new location such that: - The x-coordinate is negated (multiplied by -1). - The y-coordinate remains the same. This transformation results in a mirror image of the figure along the y-axis.
Transcribed Image Text:**Translation and Reflection in Mathematics** **Translation:** In this exercise, point 17 describes a translation on the coordinate plane. The translation is defined by the transformation: \[ (x, y) \rightarrow (x, y - 1) \] This means that every point on the plane is moved one unit downward, parallel to the y-axis. The x-coordinate remains unchanged, while the y-coordinate is decreased by 1. **Reflection:** Reflection in this context refers to flipping a figure over a specific line. Here, the reflection is in the y-axis. This operation takes each point on the plane and maps it to a new location such that: - The x-coordinate is negated (multiplied by -1). - The y-coordinate remains the same. This transformation results in a mirror image of the figure along the y-axis.
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