Chapter 9.1, Problem 9CYU

To determine

To find: The correct option for the distance the kiosk from the eyeglass store.

Answer to Problem 9CYU

The correct option is A.

Explanation of Solution

Given:

The given coordinates are:

The ice cream store is at $\left(2,4\right)$ .

The eyeglass store is at $\left(78,46\right)$ .

As the kiosk for the cell phone is halfway between the ice creamery and the see clearly eyeglass.

So kiosk is at the midpoint of given coordinates first, it is need to find the midpoint $M\left(x,y\right)$ .

The midpoint of two points is given as:

  $M\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

The midpoint is calculated as:

  $\begin{array}{c}M\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\\ =\left(\frac{2+\left(78\right)}{2},\frac{4+\left(46\right)}{2}\right)\\ =\left(40,25\right)\end{array}$

Therefore the midpoint is $\left(40,25\right)$ .

Now it is need to find distance between the points $\left(40,25\right)\&\left(78,46\right)$ .

Now the distance between each pair of points with the given coordinates is given as:

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

The distance the kiosk from the eyeglass store is calculated as:

  $\begin{array}{c}d=\sqrt{{\left(78-40\right)}^2+{\left(46-25\right)}^2}\\ =\sqrt{{\left(1444\right)}^2+{\left(441\right)}^2}\\ =\sqrt{1882}\\ \approx 43.38\end{array}$

Therefore the approximately distance the kiosk from the eyeglass store is $43.4$ units.