Farley rides 22 miles each day
.
<h3><u>Explanation:
</u></h3>
Let us take the 4 points as A(-4,3), B (-4,0), C (4,0) and D (4,3).
Let us consider that each unit on a plane is 1 mile. So in order to calculate how far did Farley rode, we need to calculate all the 4 distances, which are A to B, B to C, C to D, and D to A.
Distance between two points P(x1,y1) and Q(x2,y2) is given by:
d (P, Q) = ![\sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28x_2-x_1%29%5E%7B2%7D%20%2B%20%28y_2-y_1%29%5E%7B2%7D%7D)
Distance A to B:
We need to calculate the distance between these two coordinates (-4,3) and (-4,0).
d (A, B) = ![\sqrt{(-4-(-4))^{2} + (0-(-3))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4-%28-4%29%29%5E%7B2%7D%20%2B%20%280-%28-3%29%29%5E%7B2%7D%7D)
d (A, B) = ![\sqrt{(-4+4))^{2} + (0+3))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4%2B4%29%29%5E%7B2%7D%20%2B%20%280%2B3%29%29%5E%7B2%7D%7D)
d (A, B) = ![\sqrt{(0)^{2} + (3)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%280%29%5E%7B2%7D%20%2B%20%283%29%5E%7B2%7D%7D)
d (A, B) = ![\sqrt{(3)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%283%29%5E%7B2%7D%7D)
d (A, B) = ![\sqrt{(9)}](https://tex.z-dn.net/?f=%5Csqrt%7B%289%29%7D)
d (A, B) = 3
Distance B to C:
We need to calculate the distance between these two coordinates (-4,0) and (4,0).
d (B, C) =![\sqrt{(4-(-4))^{2} + (0-0)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%284-%28-4%29%29%5E%7B2%7D%20%2B%20%280-0%29%5E%7B2%7D%7D)
d (B, C) = ![\sqrt{(4+4))^{2} + (0))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%284%2B4%29%29%5E%7B2%7D%20%2B%20%280%29%29%5E%7B2%7D%7D)
d (B, C) = ![\sqrt{(8)^{2} + (0)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%288%29%5E%7B2%7D%20%2B%20%280%29%5E%7B2%7D%7D)
d (B, C) = ![\sqrt{(8)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%288%29%5E%7B2%7D%7D)
d (B, C) = ![\sqrt{(16)}](https://tex.z-dn.net/?f=%5Csqrt%7B%2816%29%7D)
d (B, C) = 8
Distance C to D:
We need to calculate the distance between these two coordinates (4,0) and (4,3).
d (C, D) = ![\sqrt{(4-(4))^{2} + (3-0)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%284-%284%29%29%5E%7B2%7D%20%2B%20%283-0%29%5E%7B2%7D%7D)
d (C, D) = ![\sqrt{(0))^{2} + (3))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%280%29%29%5E%7B2%7D%20%2B%20%283%29%29%5E%7B2%7D%7D)
d (C, D) = ![\sqrt{(0) + (9)}](https://tex.z-dn.net/?f=%5Csqrt%7B%280%29%20%2B%20%289%29%7D)
d (C, D) = ![\sqrt{(9)}](https://tex.z-dn.net/?f=%5Csqrt%7B%289%29%7D)
d (C, D) = 3
Distance D to A:
We need to calculate the distance between these two coordinates (4,3) and (-4,3).
d (D, A) = ![\sqrt{(-4-(4))^{2} + (3-3)^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-4-%284%29%29%5E%7B2%7D%20%2B%20%283-3%29%5E%7B2%7D%7D)
d (D, A) = ![\sqrt{(-8))^{2} + (0))^{2}}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-8%29%29%5E%7B2%7D%20%2B%20%280%29%29%5E%7B2%7D%7D)
d (D, A) = ![\sqrt{(64) + (0)}](https://tex.z-dn.net/?f=%5Csqrt%7B%2864%29%20%2B%20%280%29%7D)
d (D, A) = ![\sqrt{(64)}](https://tex.z-dn.net/?f=%5Csqrt%7B%2864%29%7D)
d (D, A) = 8
Farley's daily distance = d (A, B) + d (B, C) + d (C, D) + d (D, A) = 3 + 8 + 3 + 8 = 22 miles.