Question

One airplane is located 200 km north and 50 km east of an airport. A second plane at the same altitude is located 30 km north and 100 km north and 100 km west.

The distance between the planes is closest to:
A. 150 km
B. 200 km
C. 300 km
D. 350 km
E. 400 km

Answer 1

Answer: B

Explanation:

We can define the North as our positive y-axis, and the East as the positive x-axis.

The position of the airport is the (0, 0)

Then the position of the first plane is: (200 km north and 50 km east)

(50km, 200km)

The position of the other plane is: (30 km north and 100 km west)

(-100km, 30km)

Now, if we have two points (a, b) and (c, d)

The distance between those points is:

D = √( (a - c)^2 + (b - d)^2)

Then the distance between the planes is:

D = √( (50km - (-100km))^2 + (200km - 30km)^2)

D = √( (150km)^2 + (170km)^2)

D = 226.7km

Then the distance is closest to 200km, the correct option is B.