Chapter 9, Problem 5STP

To determine

To find: The distance between the garden and the rope swing.

Answer to Problem 5STP

The distance between the garden and the rope swing is $74\text{feet}$ and correct option is $\text{A}$ .

Explanation of Solution

Given information:

The mom’s garden point $G\left(-4,-6\right)$ .

The rope swing is at point $S\left(3,7\right)$ .

Calculation:

Using the distance formula between two co-ordinates $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is as.

  $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Substitute the value in above equation.

  $\begin{array}{c}d=\sqrt{{\left(3-\left(-4\right)\right)}^2+{\left(7-\left(-6\right)\right)}^2}\\ =\sqrt{{\left(7\right)}^2+{\left(13\right)}^2}\\ =\sqrt{49+169}\\ =\sqrt{218}=14\cdot 76482306\text{unit}\end{array}$

Scale of the map is $1\text{unit}=5\text{feet}$ .

The actual distance between garden and the rope swing is.

  $\begin{array}{c}14\cdot 76482306\times 5=73\cdot 82411530\text{feet}\\ \approx 74\text{feet}\end{array}$

The approximate distance between the garden and the rope swim is $74\text{feet}$ .

Therefore, the distance between the garden and the rope swing is $74\text{feet}$ and correct option is $\text{A}$ .