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 (130, 105). Finally he needs to fly back to the Daily Planet to get back to work as "Clark Kent'. What is the total distance for the trip?

Answer 1

Given:

Superman is working at Daily Planet Newspaper P(100, 40).

Bank robbery at B(40,80).

Criminals to jail at C(130, 105).

Then fly back to the Daily Planet.

To find:

The total distance for the trip.

Solution:

Distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula, the distance between Daily Planet Newspaper P(100, 40) and place of bank robbery at B(40,80) is

$PB=\sqrt{(40-100)^2+(80-40)^2}$

$PB=\sqrt{(-60)^2+(40)^2}$

$PB=\sqrt{3600+1600}$

$PB=\sqrt{5200}$

$PB=20\sqrt{13}$

Similarly,

Distance between place of bank robbery at B(40,80) and jail at C(130,105) is

$BC=\sqrt{\left(130-40\right)^2+\left(105-80\right)^2}$

$BC=5\sqrt{349}$

Distance between jail at C(130,105) and Daily Planet Newspaper P(100, 40) is

$CP=\sqrt{\left(100-130\right)^2+\left(40-105\right)^2}$

$CP=5\sqrt{205}$

Total distance for the trip = PB+ BC +CP

$Trip=2\sqrt{13}+5\sqrt{349}+5\sqrt{205}$

$Trip=7.2111+93.4077+71.5891$

$Trip=172.2079$

$Trip\approx 172.21$

Therefore, the total distance for the trip is about 172.21 units.