Chapter 10.1, Problem 10E

To determine

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

Answer to Problem 10E

The coordinates of the points $\text{A}$ , $\text{B}$ and $\text{C}$ are $\left(6,2,-6\right)$ , $\left(2,-1,2\right)$ and $\left(-2,3,0\right)$ respectively.

Explanation of Solution

Given information:

The graph is given below.

  

Calculation:

First consider the point $\text{A}$ , As the point $\text{A}$ is $6$ units in front of $yz$ plane and $2$ 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 $6$ , $2$ and $-6$ respectively.

Now consider the point $\text{B}$ , As the point $\text{B}$ is $2$ units in front of $yz$ plane and $1$ units to the left of $xz$ plane and $2$ units above the $xy$ plane. So, the $x$ , $y$ and $z$ coordinates of the point $\text{B}$ are $2$ , $-1$ and $2$ respectively.

Now consider the point $\text{C}$ , As the point $\text{C}$ is $2$ units behind the $yz$ plane and $3$ units to the right of $xz$ plane and $0$ units below the $xy$ plane. So, the $x$ , $y$ and $z$ coordinates of the point $\text{C}$ are $-2$ , $3$ and $0$ respectively.

Therefore, the coordinates of the points $\text{A}$ , $\text{B}$ and $\text{C}$ are $\left(6,2,-6\right)$ , $\left(2,-1,2\right)$ and $\left(-2,3,0\right)$ respectively.