A computer software exists so that the cursor of the program and ends at the origin of the plane. A program is written to draw a triangle with vertices A (1,4), B (6,2), and C (3,1) so that the cursor only moves in straight lines and travels from the origin to A, then to B, then to C, then to A, and then back "home" to the origin. 1) plot the points on the coordinate plane. 3) What is the approximate total distance traveled by the cursor? Be sure to show your work and explain your answer.
A computer software exists so that the cursor of the program and ends at the origin of the plane. A program is written to draw a triangle with vertices A (1,4), B (6,2), and C (3,1) so that the cursor only moves in straight lines and travels from the origin to A, then to B, then to C, then to A, and then back "home" to the origin. 1) plot the points on the coordinate plane. 3) What is the approximate total distance traveled by the cursor? Be sure to show your work and explain your answer.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.1: Systems Of Equations
Problem 61E
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![**Title: Calculating Distance Traveled by a Triangle Plotting Program**
**Description:**
In this exercise, we will use a computer software program designed to move a cursor on a coordinate plane. This program begins at the origin (0,0) and is written to draw a triangle with specified vertices. The cursor travels in straight lines between the points.
**Task Details:**
1. **Plotting the Points:**
- Vertex **A** is at coordinates **(1,4)**
- Vertex **B** is at coordinates **(6,2)**
- Vertex **C** is at coordinates **(3,1)**
2. **Path of the Cursor:**
- The cursor starts at the origin **(0,0)**.
- Moves to **A** (1, 4)
- Continues to **B** (6, 2)
- Moves to **C** (3, 1)
- Returns to **A** (1, 4)
- Finally returns "home" to the origin **(0,0)**
**Questions:**
1. **Plot the points on the coordinate plane.**
2. **What is the approximate total distance traveled by the cursor? Be sure to show your work and explain your answer.**
**Explanation:**
To find the total distance traveled, calculate the distance between each pair of points using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
**Steps to Calculate Distances:**
1. **From Origin to A:**
\( d_{OA} = \sqrt{(1-0)^2 + (4-0)^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.12 \)
2. **From A to B:**
\( d_{AB} = \sqrt{(6-1)^2 + (2-4)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.39 \)
3. **From B to C:**
\( d_{BC} = \sqrt{(3-6)^2 + (1-2)^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3829f931-9257-40ee-99af-de1dd428439e%2F7641c34e-57dc-4db8-a7ac-236d282fb072%2Fvj0g6ur_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Distance Traveled by a Triangle Plotting Program**
**Description:**
In this exercise, we will use a computer software program designed to move a cursor on a coordinate plane. This program begins at the origin (0,0) and is written to draw a triangle with specified vertices. The cursor travels in straight lines between the points.
**Task Details:**
1. **Plotting the Points:**
- Vertex **A** is at coordinates **(1,4)**
- Vertex **B** is at coordinates **(6,2)**
- Vertex **C** is at coordinates **(3,1)**
2. **Path of the Cursor:**
- The cursor starts at the origin **(0,0)**.
- Moves to **A** (1, 4)
- Continues to **B** (6, 2)
- Moves to **C** (3, 1)
- Returns to **A** (1, 4)
- Finally returns "home" to the origin **(0,0)**
**Questions:**
1. **Plot the points on the coordinate plane.**
2. **What is the approximate total distance traveled by the cursor? Be sure to show your work and explain your answer.**
**Explanation:**
To find the total distance traveled, calculate the distance between each pair of points using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
**Steps to Calculate Distances:**
1. **From Origin to A:**
\( d_{OA} = \sqrt{(1-0)^2 + (4-0)^2} = \sqrt{1 + 16} = \sqrt{17} \approx 4.12 \)
2. **From A to B:**
\( d_{AB} = \sqrt{(6-1)^2 + (2-4)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.39 \)
3. **From B to C:**
\( d_{BC} = \sqrt{(3-6)^2 + (1-2)^2} = \sqrt{9 + 1} = \sqrt{10} \approx 3.
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