Answer:
34.6 units
Step-by-step explanation:
The lenght of fencing required is the total distance between point A to B, B to C, C to D, and D to A. That is the distance between all 4 corners of the meadow.
The coordinates of the corners of the meadow is shown on a coordinate plane in the attachment. (See attachment below).
Let's use the distance formula to calculate the distance between the 4 corners of the meadow using their coordinates as follows:
Distance between point A(-6, 2) and point B(2, 6):
[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] A(-6, 2)) = (x_1, y_1) [/tex]
[tex] B(2, 6) = (x_2, y_2) [/tex]
[tex] AB = \sqrt{(2 - (-6))^2 + (6 - 2)^2} [/tex]
[tex] AB = \sqrt{(8)^2 + (4)^2} [/tex]
[tex] AB = \sqrt{64 + 16} = \sqrt{80} [/tex]
[tex] AB = 8.9 [/tex] (nearest tenth)
Distance between B(2, 6) and C(7, 1):
[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] B(2, 6) = (x_1, y_1) [/tex]
[tex] C(7, 1) = (x_2, y_2) [/tex]
[tex] BC = \sqrt{(7 - 2)^2 + (1 - 6)^2} [/tex]
[tex] BC = \sqrt{(5)^2 + (-5)^2} [/tex]
[tex] BC = \sqrt{25 + 25} = \sqrt{50} [/tex]
[tex] BC = 7.1 [/tex] (nearest tenth)
Distance between C(7, 1) and D(3, -5):
[tex] CD = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] C(7, 1) = (x_1, y_1) [/tex]
[tex] D(3, -5) = (x_2, y_2) [/tex]
[tex] CD = \sqrt{(3 - 7)^2 + (-5 - 1)^2} [/tex]
[tex] CD = \sqrt{(-4)^2 + (-6)^2} [/tex]
[tex] CD = \sqrt{16 + 36} = \sqrt{52} [/tex]
[tex] CD = 7.2 [/tex] (nearest tenth)
Distance between D(3, -5) and A(-6, 2):
[tex] DA = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]
Let,
[tex] D(3, -5) = (x_1, y_1) [/tex]
[tex] A(-6, 2) = (x_2, y_2) [/tex]
[tex] DA = \sqrt{(-6 - 3)^2 + (2 - (-5))^2} [/tex]
[tex] DA = \sqrt{(-9)^2 + (7)^2} [/tex]
[tex] DA = \sqrt{81 + 49} = \sqrt{130} [/tex]
[tex] DA = 11.4 [/tex] (nearest tenth)
Length of fencing required = 8.9 + 7.1 + 7.2 + 11.4 = 34.6 units
