Chapter 15.2, Problem 25PSC

To determine

To explain the reasoning of each student.

Explanation of Solution

Given:

The given figure is-

  

Spider crawled from point $(2,0,8)$ to the point $(5,10,0)$ .

Calculation:

Abigail said the shortest distance the spider has taken is $12+\sqrt{89}$ .

Reasoning: Abigail is calculating the shortest distance between the point obtained midway between $(2,0,8)$ and $(6,0,0)$ and the point $(5,10,0)$ .

  $\begin{array}{l}2\times 6+\sqrt{8^2+5^2}\\ =12+\sqrt{89}\end{array}$

Ben said the shortest distance the spider has taken is $10+\sqrt{125}$ .

Reasoning: Ben is calculating the shortest distance between the point obtained midway between $(2,0,8)$ and $(5,10,0)$ and the point $(6,0,0)$ .

  $\begin{array}{l}2\times 5+\sqrt{5^2+{10}^2}\\ =10+\sqrt{125}\end{array}$

Carol said the shortest distance the spider has taken is $8+\sqrt{109}$ .

Reasoning:

Reasoning: Ben is calculating the shortest distance between the point obtained midway between $(5,10,0)$ and $(6,0,0)$ and the point $(2,0,8)$ .

  $\begin{array}{l}8+\sqrt{1^2+{10}^2+8}\\ =8+\sqrt{101}\end{array}$

Deanna responded that the actual shortest distance is $16.40$ .

The correct result is the distance of the dotted line.