Chapter 10.1, Problem 12E

To determine

To find: The approximate coordinates of the points $\text{A},\text{B},\text{C}$ in the given graph.

Answer to Problem 12E

The coordinates of the points $\text{A}$ , $\text{B}$ and $\text{C}$ are $\left(0,5,-6\right)$ , $\left(5,4,-4\right)$ and $\left(-4,1,8\right)$ respectively.

Explanation of Solution

Given information:

The graph is given below.

  

Calculation:

First consider the point $\text{A}$ , As the point $\text{A}$ is $0$ units in front of $yz$ plane and $5$ units to the right of $xz$ plane and $6$ units below the $xy$ plane. So, the $x$ , $y$ and $z$ coordinates of the point $\text{A}$ are $0$ , $5$ and $-6$ respectively.

Now consider the point $\text{B}$ , As the point $\text{B}$ is $5$ units in front of $yz$ plane and $4$ units to the left of $xz$ plane and $4$ units below the $xy$ plane. So, the $x$ , $y$ and $z$ coordinates of the point $\text{B}$ are $5$ , $4$ and $-4$ respectively.

Now consider the point $\text{C}$ , As the point $\text{C}$ is $4$ units behind the $yz$ plane and $1$ units to the right of $xz$ plane and $8$ units above the $xy$ plane. So, the $x$ , $y$ and $z$ coordinates of the point $\text{C}$ are $-4$ , $1$ and $8$ respectively.

Therefore, the coordinates of the points $\text{A}$ , $\text{B}$ and $\text{C}$ are $\left(0,5,-6\right)$ , $\left(5,4,-4\right)$ and $\left(-4,1,8\right)$ respectively.