Respuesta :
Farley rides 22 miles each day .
Explanation:
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) = [tex]\sqrt{(x_2-x_1)^{2} + (y_2-y_1)^{2}}[/tex]
Distance A to B:
We need to calculate the distance between these two coordinates (-4,3) and (-4,0).
d (A, B) = [tex]\sqrt{(-4-(-4))^{2} + (0-(-3))^{2}}[/tex]
d (A, B) = [tex]\sqrt{(-4+4))^{2} + (0+3))^{2}}[/tex]
d (A, B) = [tex]\sqrt{(0)^{2} + (3)^{2}}[/tex]
d (A, B) = [tex]\sqrt{(3)^{2}}[/tex]
d (A, B) = [tex]\sqrt{(9)}[/tex]
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) =[tex]\sqrt{(4-(-4))^{2} + (0-0)^{2}}[/tex]
d (B, C) = [tex]\sqrt{(4+4))^{2} + (0))^{2}}[/tex]
d (B, C) = [tex]\sqrt{(8)^{2} + (0)^{2}}[/tex]
d (B, C) = [tex]\sqrt{(8)^{2}}[/tex]
d (B, C) = [tex]\sqrt{(16)}[/tex]
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) = [tex]\sqrt{(4-(4))^{2} + (3-0)^{2}}[/tex]
d (C, D) = [tex]\sqrt{(0))^{2} + (3))^{2}}[/tex]
d (C, D) = [tex]\sqrt{(0) + (9)}[/tex]
d (C, D) = [tex]\sqrt{(9)}[/tex]
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) = [tex]\sqrt{(-4-(4))^{2} + (3-3)^{2}}[/tex]
d (D, A) = [tex]\sqrt{(-8))^{2} + (0))^{2}}[/tex]
d (D, A) = [tex]\sqrt{(64) + (0)}[/tex]
d (D, A) = [tex]\sqrt{(64)}[/tex]
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.
