Superman is working at the Daily Planet Newspaper P (100, 40). He needs to fly to stop a bank robbery at B (40, 80) and then bring the criminals to jail at J (130, 105)................

Question

Superman is working at the Daily Planet Newspaper P (100, 40). He needs to fly to stop a bank robbery at B (40, 80) and then bring the criminals to jail at J (130, 105). Finally he needs to fly back to the Daily Planet toget back to work as ‘Clark Kent’. What is the total distance for the trip?

I need help.

Answer 1

Hi Bee,

Let d1, d2, and d3, denote the distance over the 3 legs of the trip:

d1: P to B, d2: B to J, d3: J to P.

For the first trip, he travels from P (100, 40) to B (40, 80). That means he traveled 40-100=-60 in the x direction and 80-40=40 in the y direction. Using the Pythagorean theorem, he has traveled:

d1 = sqrt(Δx²+Δy²) = sqrt((-60)²+(40)²) = 72.111

In the same way,

d2 = sqrt(Δx²+Δy²) = sqrt((90)²+(25)²) = 93.408

d3 = sqrt(Δx²+Δy²) = sqrt((-30)²+(-65)²) = 71.589

Adding these all up for the total trip,

d = d1+d2+d3 = 237.11

I hope that helps.

BR,

Omar

Answer 2

You will utilize the distance formula between two points to calculate each of the legs he flew, then add them all together.

1. Distance formula: d = √((x₂ – x₁)² + (y₂-y₁)²)
2. points: (100, 40), (40,80), (130, 105) (then back to (100,40)
3. √(100-40)² + (40-80)² = √5200 = 72.11 Leg 1
4. √(40-130)² + (80-105)² = √8725 = 93.41 Leg 2
5. √(130-100)² + (105-40)² = √5125 = 71.59 Leg 3
6. Add all three legs to get the total distance = 237.11

I hope this helps you!

Answer 3

I'm using a rt triangle formula: a^2+b^2=c^2.

Stating at 100, 40; going to 40,80; so a=80-40=40; b=100-40=60. This length is 1600+3600=5200^.5=72.11mi.

From 40,80 to 130,105; a=25; b=90; so 625+8100=8725^.5= 93.41mi.

From 130,105 to 100,40; a=30; b=65; so 900+4225=5125^.5= 71.59mi.

=237.1078......mi.