Chapter 13.1, Problem 34WE

(a)

To determine

To find: The twelve points, each with integer coordinates.

Answer to Problem 34WE

The twelve points from the point $\left(-8,1\right)$ are given below.

Explanation of Solution

Given information:

The coordinates are $5$ units from $\left(-8,1\right)$ .

Calculation:

Consider the coordinates $\left(-8,1\right)$ ,

  

Figure- $\left(1\right)$ .

Add the suitable points to get the points that are $5$ units from $\left(-8,1\right)$ .

Calculate the first point.

  $\begin{array}{l}{C}_1=\left(-8,1\right)+\left(0,5\right)\\ C_1=\left(-8,-6\right)\end{array}$

Calculate the second point.

  $\begin{array}{l}{C}_2=\left(-8,1\right)+\left(0,-5\right)\\ C_2=\left(-8,-4\right)\end{array}$

Calculate the third point.

  $\begin{array}{l}{C}_3=\left(-8,1\right)+\left(-3,4\right)\\ C_3=\left(-11,5\right)\end{array}$

Calculate the fourth point.

  $\begin{array}{l}{C}_4=\left(-8,1\right)+\left(-3,-4\right)\\ C_4=\left(-11,-3\right)\end{array}$

Calculate the fifth point.

  $\begin{array}{l}{C}_5=\left(-8,1\right)+\left(-4,3\right)\\ C_5=\left(-12,4\right)\end{array}$

Calculate the sixth point.

  $\begin{array}{l}{C}_6=\left(-8,1\right)+\left(-4,-3\right)\\ C_6=\left(-12,-2\right)\end{array}$

Calculate the seventh point.

  $\begin{array}{l}{C}_7=\left(-8,1\right)+\left(5,0\right)\\ C_7=\left(-3,1\right)\end{array}$

Calculate the eighth point.

  $\begin{array}{l}{C}_8=\left(-8,1\right)+\left(-5,0\right)\\ C_8=\left(-13,1\right)\end{array}$

Calculate the night point.

  $\begin{array}{l}{C}_9=\left(-8,1\right)+\left(4,3\right)\\ C_9=\left(-4,4\right)\end{array}$

Calculate the tenth point.

  $\begin{array}{l}{C}_{10}=\left(-8,1\right)+\left(4,-3\right)\\ C_{10}=\left(-4,-2\right)\end{array}$

Calculate the eleventh point.

  $\begin{array}{l}{C}_{11}=\left(-8,1\right)+\left(3,4\right)\\ C_{11}=\left(-5,5\right)\end{array}$

Calculate the twelfths point.

  $\begin{array}{l}{C}_{12}=\left(-8,1\right)+\left(3,-4\right)\\ C_{12}=\left(-5,-3\right)\end{array}$

Therefore, the twelve points from the point $\left(-8,1\right)$ are given.

(b)

To determine

To find: An equation of the circle containing these points.

Answer to Problem 34WE

The equation of the point $\left(-8,1\right)$ is ${(x+8)}^2+{\left(y-1\right)}^2=25$ .

Explanation of Solution

Given information:

Given that the coordinates are $5$ units from $\left(-8,1\right)$ .

Calculation:

Consider the coordinates $\left(-8,1\right)$ .

  

Figure- $\left(1\right)$ .

Write the equation of circle.

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

Substitute the values.

  $\begin{array}{}$ {(x+8)}^2+{\left(y-1\right)}^2=5^2$$ {(x+8)}^2+{\left(y-1\right)}^2=25$\end{array}$

Therefore, the equation of the point $\left(-8,1\right)$ is ${(x+8)}^2+{\left(y-1\right)}^2=25$ .