Question

While riding their dirt bikes in a desert wilderness park, Bud and Travis realize they are lost. They send out a GPS distress signal that is picked up by a dispatcher at the park entrance. The dispatcher pinpoints their location at 14 miles north and 4 miles east of the park entrance. Search and rescue teams from Station One, 8 miles west and 2 miles south of the park entrance, and Station Two, 9 miles east and 2 miles north of the park entrance, will be sent to help them. The origin describes the entrance of the park.



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Part A) What is the distance between the entrance of the Park and Bud and Travis?



Part B) What is the distance between Station 2 and Bud and Travis?

Answer 1

Answer

part a answer: 14.6=c

part b answer:28,561

Step-by-step explanation:

part a: 4^2 + 14^2     16+196=212       212^2=c     14.6=c

part b: 5^2+12^2=c^2  25+144=c^2 169=c  169^2  c=28,561

Answer 2

The distance between the entrance of the Park and Bud and Travis is 14.56 mi, and the distance between Station 2 and Bud and Travis is 13 mi.

What is the distance between the entrance of the Park and Bud and Travis?

Let's say that the entrance is the point (0, 0).

And from that reference point, the location of the kids is at (4mi, 14mi)

(where north is on the y-axis and east on the x-axis).

So the distance between these two points is:

$d = \sqrt{(4mi - 0mi)^2 + (14mi - 0mi)^2} = 14.56 mi$

What is the distance between Station 2 and Bud and Travis?

We know that location 2 is on the point (9mi, 2mi), and the kids are at  (4mi, 14mi), then the distance is given by:

$d = \sqrt{(9mi - 4mi)^2 + (14mi - 2mi)^2} = 13mi$

This time the distance is 13 miles.

If you want to learn more about distances:

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