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

Answer:

The perimeter is 14 units

Step-by-step 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:

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

For AB

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

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

$AB = \sqrt{(-2 - 1)^2 + (2 - 2)^2} = \sqrt{9} = 3$

For BC

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

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

$BC = \sqrt{(1-1)^2 + (2--2)^2} = \sqrt{16} = 4$

For CD

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

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

$CD = \sqrt{(1 - -2)^2 + (-2 -- 2)^2} = \sqrt{9} = 3$

For DA

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

$A = (-2,2)$  --- $(x_2,y_2)$

$DA = \sqrt{(-2--2)^2 + (-2-2)^2} = \sqrt{16} = 4$

So, the perimeter (P) is:

$P = AB + BC + CD + DA$

$P = 3 +4 + 3 + 4$

$P = 14$

The perimeter is 14 units