Calculate the approximate Euclidean distance between the customer and the supplier, whose coordinates are given in the table below: y Customer 10 23 Supplier 13 19

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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**Problem Statement:**

Calculate the approximate Euclidean distance between the customer and the supplier, whose coordinates are given in the table below:

**Coordinates Table:**

|           | x  | y  |
|-----------|----|----|
| Customer  | 10 | 23 |
| Supplier  | 13 | 19 |

**Options:**

- 12 miles
- 7 miles
- 19 miles
- 5 miles
- 2.65 miles

**Solution Explanation:**

To calculate the Euclidean distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substituting the given coordinates:

\[ \text{Distance} = \sqrt{(13 - 10)^2 + (19 - 23)^2} \]
\[ \text{Distance} = \sqrt{3^2 + (-4)^2} \]
\[ \text{Distance} = \sqrt{9 + 16} \]
\[ \text{Distance} = \sqrt{25} \]
\[ \text{Distance} = 5 \, \text{miles} \]

Therefore, the correct answer is 5 miles.
Transcribed Image Text:**Problem Statement:** Calculate the approximate Euclidean distance between the customer and the supplier, whose coordinates are given in the table below: **Coordinates Table:** | | x | y | |-----------|----|----| | Customer | 10 | 23 | | Supplier | 13 | 19 | **Options:** - 12 miles - 7 miles - 19 miles - 5 miles - 2.65 miles **Solution Explanation:** To calculate the Euclidean distance between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Substituting the given coordinates: \[ \text{Distance} = \sqrt{(13 - 10)^2 + (19 - 23)^2} \] \[ \text{Distance} = \sqrt{3^2 + (-4)^2} \] \[ \text{Distance} = \sqrt{9 + 16} \] \[ \text{Distance} = \sqrt{25} \] \[ \text{Distance} = 5 \, \text{miles} \] Therefore, the correct answer is 5 miles.
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