Question

Sorry to be annoying again I just really suck at math and I haven't slept yet ​

Answer 1

50.33 mi.

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 =
`√((x_2 - x_1)^2 + (y_2 - y_1)^2)`

SOLUTION :-

According to question ,

On Friday , you -

• leave school and go to pizza palace. Distance travelled from school to pizza palace =
  `√((4 -(-8) )^2 + (3 - 2)^2) = √((12)^2 + (1)^2) = √(145)` ≈ 12.04 mi.
• go to movie theater after pizza palace. Distance travelled from pizza palace to movie theater =
  `√([(-4) -(-8)]^2 + (-6 - 2)^2) = √((4)^2 + (-8)^2) = √(80)= 4√(5)` ≈ 8.94 mi.
• come back to your home after the movies. Distance travelled from theater to home =
  `√([0-(-4)]^2 + (0 - 6)^2) = √((4)^2 + (-6)^2) = √(52) = 2√(13)` ≈ 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 =
  `√((7 -0 )^2 + (-5 - 0)^2) = √((7)^2 + (-5)^2) = √(74)` ≈ 8.6 mi.
• go to school after going to park. Distance travelled from park to school =
  `√((4 -7 )^2 + [3 - (-5)]^2) = √((-3)^2 + (8)^2) = √(73)` ≈ 8.54 mi.
• go to home after playing basketball in school. Distance travelled from school to home =
  `√((0 -4 )^2 + (0 - 3)^2) = √((-4)^2 + (-3)^2) = √(25)` = 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.