From his house, a man biked 3km east, 4km north, 1km east then 1km south. At that point, how far is he from his house?
To find out how far the man is from his house, we can use the concept of the Cartesian coordinate system. Let's assume the man's house is located at the origin, (0, 0).
Based on the information provided, the man first bikes 3km east, which means he moves along the positive x-axis to a point (3, 0) in the coordinate system.
Next, he bikes 4km north, which means he moves along the positive y-axis to a point (3, 4).
Then, he bikes 1km east from that point, resulting in a new position of (4, 4).
Finally, he bikes 1km south, which means he moves along the negative y-axis to a final position of (4, 3).
To find the distance between the final position and the origin (0, 0), we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values, we get:
Distance = √((4 - 0)^2 + (3 - 0)^2)
= √(4^2 + 3^2)
= √(16 + 9)
= √25
= 5
Therefore, the man is 5km away from his house at the final position.