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Given two points A(1, 8) and B(6, 14). Find the point C on the x-axis so that the total distance AC + BC is a Minimum Distance. {Draw a sketch and come up with a function for the distance. Graph the function in an appropriate window.} Give at least 3 decimal places. Minimum Total Distance of occurs when C 0) |3D DO NOT USE CALCULUS.

Given two points A(1, 8) and B(6, 14). Find the point C on the x-axis so that the total distance AC + BC is a Minimum Distance. {Draw a sketch and come up with a function for the distance. Graph the function in an appropriate window.} Give at least 3 decimal places. Minimum Total Distance of occurs when C 0) |3D DO NOT USE CALCULUS.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter9: Real Numbers And Right Triangles
Section9.5: The Distance And Midpoint Formulas
Problem 2C
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Question
**Problem Statement:** Given two points \( A(1, 8) \) and \( B(6, 14) \). **Objective:** Find the point \( C \) on the x-axis so that the total distance \( AC + BC \) is a Minimum Distance. \{Draw a sketch and come up with a function for the distance. Graph the function in an appropriate window.\} Give at least 3 decimal places. **Solution Steps:** 1. **Determine the function for the total distance \( AC + BC \):** - Use the distance formula to derive separate equations for \( AC \) and \( BC \). - Combine these equations to express the total distance as a single function of \( C \). 2. **Graphical Solution:** - Create a graph representing the total distance function. - Identify the point on the x-axis where this function reaches its minimum value. 3. **Result:** - Minimum Total Distance of \(\_\_\_\) occurs when \( C = (\_\_\_\), 0). **Note:** DO NOT USE CALCULUS. **Instructions for Completing the Problem:** 1. Calculate and plot the function graph without using calculus. 2. Look for intuitive reasoning or algebraic manipulation to localize the minimum point on the graph. This task is designed to explore the properties of geometric distances and apply graphical analysis for finding solutions.
Transcribed Image Text:**Problem Statement:** Given two points \( A(1, 8) \) and \( B(6, 14) \). **Objective:** Find the point \( C \) on the x-axis so that the total distance \( AC + BC \) is a Minimum Distance. \{Draw a sketch and come up with a function for the distance. Graph the function in an appropriate window.\} Give at least 3 decimal places. **Solution Steps:** 1. **Determine the function for the total distance \( AC + BC \):** - Use the distance formula to derive separate equations for \( AC \) and \( BC \). - Combine these equations to express the total distance as a single function of \( C \). 2. **Graphical Solution:** - Create a graph representing the total distance function. - Identify the point on the x-axis where this function reaches its minimum value. 3. **Result:** - Minimum Total Distance of \(\_\_\_\) occurs when \( C = (\_\_\_\), 0). **Note:** DO NOT USE CALCULUS. **Instructions for Completing the Problem:** 1. Calculate and plot the function graph without using calculus. 2. Look for intuitive reasoning or algebraic manipulation to localize the minimum point on the graph. This task is designed to explore the properties of geometric distances and apply graphical analysis for finding solutions.
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