Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane. (-1,-1) +++11 -4-29 2 C (-2,-4) Original Point 2 units (2,-3) Xx → Translated Point
Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane. (-1,-1) +++11 -4-29 2 C (-2,-4) Original Point 2 units (2,-3) Xx → Translated Point
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Translation of a Polygon in the Coordinate Plane
**Problem Statement:**
Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane.
**Diagram Description:**
There is an image showing a triangle with its vertices in the Cartesian plane. The original vertices of the triangle are labeled as \((-1, -1)\), \((-2, -4)\), and \((2, -3)\). The translation is specified by two arrows: moving the triangle 5 units up and 2 units to the right.
The new position of the vertices is depicted after the translation is applied.
**Translation Process:**
To translate each vertex of the polygon, apply the following mathematical operation to each coordinate:
\[ (x', y') = (x + 2, y + 5) \]
Where \((x', y')\) are the coordinates after translation, and \((x, y)\) are the original coordinates.
**Table of Coordinates:**
The table below shows the original points and the translated points:
| Original Point | Translated Point |
|:--------------:|:----------------:|
| (-1, -1) | (x, y) = (4, 1) |
| (-2, -4) | (x, y) = ( ) |
| (2, -3) | (x, y) = ( ) |
- The calculation for the first point \((-1, -1)\) was performed inaccurately as `(4, 1)` which should instead be corrected.
**Detailed Computation:**
1. For the point \((-1, -1)\):
- \( x' = -1 + 2 = 1 \)
- \( y' = -1 + 5 = 4 \)
- Corrected Translated Point: \( (1, 4) \)
2. For the point \((-2, -4)\):
- \( x' = -2 + 2 = 0 \)
- \( y' = -4 + 5 = 1 \)
- Translated Point: \( (0, 1) \)
3. For the point \((2, -3)\):
- \( x' = 2 + 2 = 4 \)
- \( y' = -3 + 5 = 2 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F418d047f-d07f-4bcf-8222-49ade4ace622%2Fc574b44b-6b8b-41c3-9c50-c9668ad5b19a%2Fpvf9jo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Translation of a Polygon in the Coordinate Plane
**Problem Statement:**
Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane.
**Diagram Description:**
There is an image showing a triangle with its vertices in the Cartesian plane. The original vertices of the triangle are labeled as \((-1, -1)\), \((-2, -4)\), and \((2, -3)\). The translation is specified by two arrows: moving the triangle 5 units up and 2 units to the right.
The new position of the vertices is depicted after the translation is applied.
**Translation Process:**
To translate each vertex of the polygon, apply the following mathematical operation to each coordinate:
\[ (x', y') = (x + 2, y + 5) \]
Where \((x', y')\) are the coordinates after translation, and \((x, y)\) are the original coordinates.
**Table of Coordinates:**
The table below shows the original points and the translated points:
| Original Point | Translated Point |
|:--------------:|:----------------:|
| (-1, -1) | (x, y) = (4, 1) |
| (-2, -4) | (x, y) = ( ) |
| (2, -3) | (x, y) = ( ) |
- The calculation for the first point \((-1, -1)\) was performed inaccurately as `(4, 1)` which should instead be corrected.
**Detailed Computation:**
1. For the point \((-1, -1)\):
- \( x' = -1 + 2 = 1 \)
- \( y' = -1 + 5 = 4 \)
- Corrected Translated Point: \( (1, 4) \)
2. For the point \((-2, -4)\):
- \( x' = -2 + 2 = 0 \)
- \( y' = -4 + 5 = 1 \)
- Translated Point: \( (0, 1) \)
3. For the point \((2, -3)\):
- \( x' = 2 + 2 = 4 \)
- \( y' = -3 + 5 = 2 \)
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