Chapter 1.3, Problem

(a)

To determine

To Find: The latitude and the longitude of the midpoint of the segment between Wilmington and Winston-Salem.

Answer

The latitude and the longitude of the midpoint is $\left(35.2°,79.05°\right)$ .

Explanation of Solution

Given:

The Wilmington, North Carolina, is located at $\left({34.3}^{\circ },{77.9}^{\circ }\right)$ , which represents north latitude and west longitude. Winston-Salem is in the northern part of the state at $\left({36.1}^{\circ },{80.2}^{\circ }\right)$ .

The given map is shown in Figure 1

  

Figure 1

Calculation:

Consider the mid-point of $\left(34.3°,77.9°\right)$ and $\left(36.1°,80.2°\right)$ is obtained as,

  $\begin{array}{c}M=\left(\frac{34.3°+36.1°}{2}\right)\left(\frac{77.9°+80.2°}{2}\right)\\ =\left(35.2°,79.05°\right)\end{array}$

(b)

To determine

To Find: Thecity neat to the location to the midpoint.

Answer

The city at the midpoint is Spring lake.

Explanation of Solution

From the graph the city that is at the midpoint is the city at the coordinates $\left(35.2°,79.05°\right)$ that is Spring lake.

(c)

To determine

To Find: The latitude and the longitude of the other point.

Answer

The coordinate of the far point is $\left(x,y\right)=\left(373.9,82.5\right)$ .

Explanation of Solution

Consider the latitude and the longitude of the midpoint is obtained as,

  $\begin{array}{l}\left(\frac{x+34.3}{2}\right)\left(\frac{y+77.9}{2}\right)=\left(36.1,80.2\right)\\ \left(x+34.3\right)\left(y+77.9\right)=\left(72.2,160.4\right)\\ \left(x,y\right)=\left(373.9,82.5\right)\end{array}$

(d)

To determine

To Find: The city near the location of the other end point.

Answer

The city at the far point is Carlisle.

Explanation of Solution

From the given map the city near $\left(x,y\right)=\left(373.9,82.5\right)$ is Carlisle.