(10 points on this) anika is hiking on a rectangular trail at the national park. there are four resting spots along the corners of the trail. one the map, they are marked with coordinates of (5, 2), (5, 4), (2, 4) and (2, 2). if each unit represents 1 mile, find the perimeter of the trail in miles using the coordinates (show work)

10 miles

Explanation: 

We define the following resting spots

A = resting spot whose coordinate is (2,2)
B = resting spot whose coordinate is (2,4)
C = resting spot whose coordinate is (5,2)
D = resting spot whose coordinate is (5,4)

If you plot A, B, C, D, you will notice that 

(Perimeter of the trail) = 2[(distance from A to C) + (distance from A to B)]

Note that A and C have the same y-coordinates (second number in their ordered pairs), so the distance from A to C is computed as the difference of their x-coordinates (first number in their ordered pairs). Thus,

(distance from A to C) = 5 - 2 = 3

Moreover, A and B have the same x-coordinates and so we compute the distance from A to B as the difference of their y-coordinates. Then,

(distance from A to B) = 4 - 2 = 2

Hence,

(Perimeter of the trail) = 2[(distance from A to C) + (distance from A to B)]
                                    = 2[2 + 3]
                                    = 2(5)
(Perimeter of the trail) = 10 miles