A person starts walking from his home. First, he goes 2 miles north and 3 miles west to a park. After spending the afternoon at the park, he walks 1 mile west and 4 miles south to a bar. How far is the bar from his home?
this can't be that hard. Just draw the lines. Starting at (0,0), he ends up at (-4,-2).
So, how far is that?
To find out how far the bar is from the person's home, we can break down the given information into a coordinate system. Let's consider the person's home as the origin (0,0) on a map.
The person starts by going 2 miles north, which means the coordinates change to (0,2). Then, the person walks 3 miles west, shifting the coordinates to (-3,2) - reaching the park.
After spending time at the park, the person walks 1 mile west, resulting in coordinates (-4,2). Finally, they walk 4 miles south, leading to coordinates (-4,-2) - arriving at the bar.
To determine the distance between the person's home and the bar, we can use the Pythagorean theorem. The formula is √(x^2 + y^2), where x and y are the differences in the x and y coordinates, respectively.
In this case, the horizontal distance (x) is -4 (going from 0 to -4), and the vertical distance (y) is -2 (going from 2 to -2).
Using the Pythagorean theorem, we calculate the distance as:
√((-4)^2 + (-2)^2) = √(16 + 4) = √20 ≈ 4.47 miles.
Therefore, the bar is approximately 4.47 miles away from the person's home.