Two hikers started at the same location. One traveled 2 miles east and then 1 mile north. The other traveled 1 mile west and then 3 miles south. At the end of their hikes, how many miles apart are the two hikers?
the answer is 5
if you use the 3,4,5 rule your answer will come out to be 5
its 5
If you use the 3,4,5 rule, the legs are 3 and 4, so the hypotenuse must be 5
To find the distance between the two hikers, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's break down the paths of the two hikers:
Hiker 1: 2 miles east and 1 mile north
Hiker 2: 1 mile west and 3 miles south
We can construct a right triangle with the starting point of the two hikers as the right angle:
Hiker 2
(1, -3)
|\
| \
| \
-------|---\-
| \
Hiker 1 (2, 1)
The horizontal distance between the two hikers is given by the difference in their horizontal coordinates (x-values), which is 2 - (-1) = 3 miles.
The vertical distance between the two hikers is given by the difference in their vertical coordinates (y-values), which is 1 - (-3) = 4 miles.
Using the Pythagorean theorem, we can calculate the distance between the two hikers:
Distance = √(3^2 + 4^2)
= √(9 + 16)
= √25
= 5 miles
Therefore, the two hikers are 5 miles apart at the end of their hikes.
consider the origin as their starting location, then the first one ends up at (2,1) and the second hiker at (-1,-3)
so, using the distance formula between 2 points :
D = √((2+1)^2 + (1+4)^2)
= √(9+25)
= √34 or appr 5.8 miles apart