Homework Help is Here – Start Your Trial Now!
Math
Geometry
**Translations and Graphs in Geometry** This section explores geometric transformations using translations. Specifically, we will graph triangle \( \triangle XYZ \) and apply successive translations to observe the changes in its position on a coordinate plane. **Triangle \( \triangle XYZ \):** - Vertex \( X \) is located at coordinates \( (2, 4) \). - Vertex \( Y \) is located at coordinates \( (6, 0) \). - Vertex \( Z \) is located at coordinates \( (7, 2) \). **Translation Steps:** 1. **First Translation:** - Formula: \((x, y) \rightarrow (x+12, y+4)\) - This moves each point 12 units to the right and 4 units up. 2. **Second Translation:** - Formula: \((x, y) \rightarrow (x-5, y-9)\) - This moves each point 5 units to the left and 9 units down. **Graph Explanation:** The graph of \( \triangle XYZ \) is plotted on a coordinate grid. The grid has x-coordinates ranging from -2 to 8 and y-coordinates ranging from -8 to 20. Each unit step is marked on both axes to facilitate accurate plotting. By applying the given translations in sequence, observe how the position of \( \triangle XYZ \) changes on the graph. This exercise demonstrates how transformations alter geometric shapes on a plane, maintaining their size and orientation but changing their location.

**Translations and Graphs in Geometry** This section explores geometric transformations using translations. Specifically, we will graph triangle \( \triangle XYZ \) and apply successive translations to observe the changes in its position on a coordinate plane. **Triangle \( \triangle XYZ \):** - Vertex \( X \) is located at coordinates \( (2, 4) \). - Vertex \( Y \) is located at coordinates \( (6, 0) \). - Vertex \( Z \) is located at coordinates \( (7, 2) \). **Translation Steps:** 1. **First Translation:** - Formula: \((x, y) \rightarrow (x+12, y+4)\) - This moves each point 12 units to the right and 4 units up. 2. **Second Translation:** - Formula: \((x, y) \rightarrow (x-5, y-9)\) - This moves each point 5 units to the left and 9 units down. **Graph Explanation:** The graph of \( \triangle XYZ \) is plotted on a coordinate grid. The grid has x-coordinates ranging from -2 to 8 and y-coordinates ranging from -8 to 20. Each unit step is marked on both axes to facilitate accurate plotting. By applying the given translations in sequence, observe how the position of \( \triangle XYZ \) changes on the graph. This exercise demonstrates how transformations alter geometric shapes on a plane, maintaining their size and orientation but changing their location.

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
See similar textbooks
icon
Related questions
Question
**Translations and Graphs in Geometry** This section explores geometric transformations using translations. Specifically, we will graph triangle \( \triangle XYZ \) and apply successive translations to observe the changes in its position on a coordinate plane. **Triangle \( \triangle XYZ \):** - Vertex \( X \) is located at coordinates \( (2, 4) \). - Vertex \( Y \) is located at coordinates \( (6, 0) \). - Vertex \( Z \) is located at coordinates \( (7, 2) \). **Translation Steps:** 1. **First Translation:** - Formula: \((x, y) \rightarrow (x+12, y+4)\) - This moves each point 12 units to the right and 4 units up. 2. **Second Translation:** - Formula: \((x, y) \rightarrow (x-5, y-9)\) - This moves each point 5 units to the left and 9 units down. **Graph Explanation:** The graph of \( \triangle XYZ \) is plotted on a coordinate grid. The grid has x-coordinates ranging from -2 to 8 and y-coordinates ranging from -8 to 20. Each unit step is marked on both axes to facilitate accurate plotting. By applying the given translations in sequence, observe how the position of \( \triangle XYZ \) changes on the graph. This exercise demonstrates how transformations alter geometric shapes on a plane, maintaining their size and orientation but changing their location.
Transcribed Image Text:**Translations and Graphs in Geometry** This section explores geometric transformations using translations. Specifically, we will graph triangle \( \triangle XYZ \) and apply successive translations to observe the changes in its position on a coordinate plane. **Triangle \( \triangle XYZ \):** - Vertex \( X \) is located at coordinates \( (2, 4) \). - Vertex \( Y \) is located at coordinates \( (6, 0) \). - Vertex \( Z \) is located at coordinates \( (7, 2) \). **Translation Steps:** 1. **First Translation:** - Formula: \((x, y) \rightarrow (x+12, y+4)\) - This moves each point 12 units to the right and 4 units up. 2. **Second Translation:** - Formula: \((x, y) \rightarrow (x-5, y-9)\) - This moves each point 5 units to the left and 9 units down. **Graph Explanation:** The graph of \( \triangle XYZ \) is plotted on a coordinate grid. The grid has x-coordinates ranging from -2 to 8 and y-coordinates ranging from -8 to 20. Each unit step is marked on both axes to facilitate accurate plotting. By applying the given translations in sequence, observe how the position of \( \triangle XYZ \) changes on the graph. This exercise demonstrates how transformations alter geometric shapes on a plane, maintaining their size and orientation but changing their location.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer