A map of a state park is drawn so that the origin is placed at the visitor center. The distance between grid lines is 1 mi, Suppose that two hikers are located at points A and B, Assume that the units of measurement are in miles,

(a) Determine the distance between the hikers,
(b) 1f the hikers want to meet for lunch, determine the location of the midpoint between the hikers,

1 answer

To solve the problem, we need the coordinates of the two points A and B where the hikers are located. Let's denote the coordinates of hiker A as \((x_1, y_1)\) and the coordinates of hiker B as \((x_2, y_2)\).

(a) Distance between the hikers:

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D Cartesian coordinate system can be calculated using the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

(b) Midpoint between the hikers:

The midpoint \(M\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) can be calculated using the midpoint formula:

\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]

To provide specific answers, please provide the coordinates of points A and B.