Answer:
50.33 mi.
Step-by-step explanation:
GIVEN :-
Coordinates of :-
- Home = (0 , 0)
- School = (4 , 3)
- Pizza place = (-8 , 2)
- Movie Theater = (-4 , -6)
- Park = (7 , -5)
TO FIND :-
- Total distance travelled on Friday & Saturday.
GENERAL FORMULAE TO BE USED IN THIS QUESTION :-
Lets say there are two points A & B on a cartesian plane whose coordinates are (x₁ , y₁) & (x₂ , y₂).
Distance between A & B = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
SOLUTION :-
According to question ,
On Friday , you -
- leave school and go to pizza palace. Distance travelled from school to pizza palace = [tex]\sqrt{(4 -(-8) )^2 + (3 - 2)^2} = \sqrt{(12)^2 + (1)^2} = \sqrt{145}[/tex] ≈ 12.04 mi.
- go to movie theater after pizza palace. Distance travelled from pizza palace to movie theater = [tex]\sqrt{[(-4) -(-8)]^2 + (-6 - 2)^2} = \sqrt{(4)^2 + (-8)^2} = \sqrt{80}= 4\sqrt{5}[/tex] ≈ 8.94 mi.
- come back to your home after the movies. Distance travelled from theater to home = [tex]\sqrt{[0-(-4)]^2 + (0 - 6)^2} = \sqrt{(4)^2 + (-6)^2} = \sqrt{52} = 2\sqrt{13}[/tex] ≈ 7.21 mi.
⇒ On Friday , total distance travelled = 12.04 + 8.94 + 7.21 = 28.19 mi.
On Saturday , you -
- go to park from your home. Distance travelled from home to park = [tex]\sqrt{(7 -0 )^2 + (-5 - 0)^2} = \sqrt{(7)^2 + (-5)^2} = \sqrt{74}[/tex] ≈ 8.6 mi.
- go to school after going to park. Distance travelled from park to school = [tex]\sqrt{(4 -7 )^2 + [3 - (-5)]^2} = \sqrt{(-3)^2 + (8)^2} = \sqrt{73}[/tex] ≈ 8.54 mi.
- go to home after playing basketball in school. Distance travelled from school to home = [tex]\sqrt{(0 -4 )^2 + (0 - 3)^2} = \sqrt{(-4)^2 + (-3)^2} = \sqrt{25}[/tex] = 5 mi.
⇒ On Saturday , total distance travelled = 8.6 + 8.54 + 5 = 22.14 mi.
∴ Total distance travelled on Friday & Saturday = 28.19 + 22.14 = 50.33 mi.
