Chapter 9.7, Problem 40PPS

To determine

To find: The coordinated of the location.

Answer to Problem 40PPS

The coordinated of the location is (4, 5)

Explanation of Solution

Given:

The dog is 10 units from the tree, 13 units from the tower and 20 units from the house.

Calculation:

The coordinates is written as,

  $\left(10,-3\right),\left(-8,10\right),\left(-12,-7\right)$

Using the distance formula, calculate the distance.

  $\begin{array}{l}\sqrt{{\left(h-10\right)}^2+{\left(k+3\right)}^2}=10\\ {\left(h-10\right)}^2+{\left(k+3\right)}^2=100\end{array}$

Using the distance formula, calculate the distance.

  $\begin{array}{l}\sqrt{{\left(h+8\right)}^2+{\left(k-10\right)}^2}=13\\ {\left(h+8\right)}^2+{\left(k-10\right)}^2=169\end{array}$

Using the distance formula, calculate the distance.

  $\begin{array}{l}\sqrt{{\left(h+12\right)}^2+{\left(k+7\right)}^2}=20\\ {\left(h+12\right)}^2+{\left(k+7\right)}^2=400\end{array}$

Draw the figure for the above equation.

  

Figure 1

From the above graph, the graph intersects at (4, 5)

Thus, the coordinated of the location is (4, 5)