Question

Anika is hiking on a rectengular trail at the nation 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 rach unit represents 1 mile find the perimiter of the trail in miles using the coordinates

Answer 1

The perimeter is 14 units

Explanation:

Given

`A = (-2,2)`

`B = (1,2)`

`C = (1,-2)`

`D = (-2,-2)`

Required

Determine the perimeter

To do this, we simply calculate the distance between the sides of the rectangle i.e. AB, BC, CD and DA.

Distance (d) is calculated using:

`d = √((x_1 - x_2)^2 + (y_1 - y_2)^2)`

For AB

`A = (-2,2)` ---
`(x_1,y_1)`

`B = (1,2)` ---
`(x_2,y_2)`

`AB = √((-2 - 1)^2 + (2 - 2)^2) = √(9) = 3`

For BC

`B = (1,2)` ---
`(x_1,y_1)`

`C = (1,-2)` ---
`(x_2,y_2)`

`BC = √((1-1)^2 + (2--2)^2) = √(16) = 4`

For CD

`C = (1,-2)` ---
`(x_1,y_1)`

`D = (-2,-2)` ---
`(x_2,y_2)`

`CD = √((1 - -2)^2 + (-2 -- 2)^2) = √(9) = 3`

For DA

`D = (-2,-2)` ---
`(x_1,y_1)`

`A = (-2,2)` ---
`(x_2,y_2)`

`DA = √((-2--2)^2 + (-2-2)^2) = √(16) = 4`

So, the perimeter (P) is:

`P = AB + BC + CD + DA`

`P = 3 +4 + 3 + 4`

`P = 14`

The perimeter is 14 units