Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane. Original Point Translated Point (-1, -1) (-2,-4) (2, -3) 4 (-1,-1)7 +++ -4-2 (-2,-4) (x, y) = (x, y) = (x, y) = 5 units |||| x 2 (2,-3) 2 units T
Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane. Original Point Translated Point (-1, -1) (-2,-4) (2, -3) 4 (-1,-1)7 +++ -4-2 (-2,-4) (x, y) = (x, y) = (x, y) = 5 units |||| x 2 (2,-3) 2 units T
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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![### Translating Points on a Coordinate Plane
In this exercise, we will explore how to find the coordinates of the vertices of a polygon after performing a translation on the coordinate plane. The translation in this case involves moving each point 2 units to the right and 5 units up.
#### Problem Statement
Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane.
**Original Point to Translated Point Table:**
| Original Point | Translated Point |
|----------------|------------------|
| (-1, -1) | (x, y) = ( ) |
| (-2, -4) | (x, y) = ( ) |
| (2, -3) | (x, y) = ( ) |
#### Diagram Description
The diagram depicts a triangle on a coordinate plane with its vertices located at the original points (-1, -1), (-2, -4), and (2, -3). Each vertex is translated 2 units to the right and 5 units up.
Details of the diagram:
1. **Axes**: The horizontal axis (x-axis) and vertical axis (y-axis) intersect at the origin (0, 0).
2. **Original Points**: The vertices of the original triangle are indicated.
- Point (-1, -1) is marked at 1 unit left and 1 unit down from the origin.
- Point (-2, -4) is marked at 2 units left and 4 units down from the origin.
- Point (2, -3) is marked at 2 units right and 3 units down from the origin.
3. **Translation Arrows**:
- Each point is translated 2 units to the right, which is shown with horizontal arrows pointing to the right.
- Each point is translated 5 units up, shown with vertical arrows pointing upwards.
To perform the translation, use the rule:
\[
(x', y') = (x + 2, y + 5)
\]
Let's apply this translation to each point:
1. **Original Point (-1, -1)**
\[
x' = -1 + 2 = 1
\]
\[
y' = -1 + 5 = 4
\]
Translated Point: (1, 4)
2. **Original Point (-2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb5ff0f4-c9f6-49ea-9161-fbb64a60fa05%2F21b648e4-c846-4695-acf4-629ea233c4dd%2F2s9cj2v_processed.png&w=3840&q=75)
Transcribed Image Text:### Translating Points on a Coordinate Plane
In this exercise, we will explore how to find the coordinates of the vertices of a polygon after performing a translation on the coordinate plane. The translation in this case involves moving each point 2 units to the right and 5 units up.
#### Problem Statement
Find the coordinates of the vertices of the polygon after the indicated translation to a new position in the plane.
**Original Point to Translated Point Table:**
| Original Point | Translated Point |
|----------------|------------------|
| (-1, -1) | (x, y) = ( ) |
| (-2, -4) | (x, y) = ( ) |
| (2, -3) | (x, y) = ( ) |
#### Diagram Description
The diagram depicts a triangle on a coordinate plane with its vertices located at the original points (-1, -1), (-2, -4), and (2, -3). Each vertex is translated 2 units to the right and 5 units up.
Details of the diagram:
1. **Axes**: The horizontal axis (x-axis) and vertical axis (y-axis) intersect at the origin (0, 0).
2. **Original Points**: The vertices of the original triangle are indicated.
- Point (-1, -1) is marked at 1 unit left and 1 unit down from the origin.
- Point (-2, -4) is marked at 2 units left and 4 units down from the origin.
- Point (2, -3) is marked at 2 units right and 3 units down from the origin.
3. **Translation Arrows**:
- Each point is translated 2 units to the right, which is shown with horizontal arrows pointing to the right.
- Each point is translated 5 units up, shown with vertical arrows pointing upwards.
To perform the translation, use the rule:
\[
(x', y') = (x + 2, y + 5)
\]
Let's apply this translation to each point:
1. **Original Point (-1, -1)**
\[
x' = -1 + 2 = 1
\]
\[
y' = -1 + 5 = 4
\]
Translated Point: (1, 4)
2. **Original Point (-2
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