Question

Anika is hiking on a rectangular trail at the national Park. There are four resting spots along the corners of the trail. On the map they are marked with coordinates of (-2,2), (1,2,) (1,-2), and (-2,-2). If each unit represents 1 mile find the perimeter of the trail in miles using the coordinates

Answer 1

Explanation:

The distance from (-2,2) to (1, 2) is the distance from x=-2 to x=1 along the line y=2. That horizontal distance is 1-(-2) = 3. The distance from (1, -2) to (-2, -2) is the same along the horizontal line y=-2.The distance from (1, 2) to (1, -2) is the distance from y=2 to y=-2 along the line x=1. That vertical distance is 2-(-2) = 4. The distance from (-2, -2) to (-2, 2) is the same along the vertical line x=-2.So, the trail has two legs of length 3 and two legs of length 4. The total length of the trail (the perimeter of the rectangle) is ... 2·3 +2·4 = 2·(3+4) = 14 . . . . miles

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Answer 2

14 miles

Explanation:

The distance from (-2,2) to (1, 2) is the distance from x=-2 to x=1 along the line y=2. That horizontal distance is 1-(-2) = 3. The distance from (1, -2) to (-2, -2) is the same along the horizontal line y=-2.

The distance from (1, 2) to (1, -2) is the distance from y=2 to y=-2 along the line x=1. That vertical distance is 2-(-2) = 4. The distance from (-2, -2) to (-2, 2) is the same along the vertical line x=-2.

So, the trail has two legs of length 3 and two legs of length 4. The total length of the trail (the perimeter of the rectangle) is ...

2·3 +2·4 = 2·(3+4) = 14 . . . . miles