A walks 2km South. Then turns West and walks 3km. Then turns North and walks 6km. Then turns East and walks 7km. Finally, turns South and walks 2km. What is the shortest distance from the starting point?
Correct: D
Let the starting point be (0,0).
1. Walks 2km South: (0, -2).
2. Turns West and walks 3km: (-3, -2).
3. Turns North and walks 6km: (-3, -2+6) = (-3, 4).
4. Turns East and walks 7km: (-3+7, 4) = (4, 4).
5. Turns South and walks 2km: (4, 4-2) = (4, 2).
His final position is (4, 2).
To find the shortest distance from the starting point (0,0) to (4,2), we use the Pythagorean theorem:
Distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Distance = sqrt((4-0)^2 + (2-0)^2)
Distance = sqrt(4^2 + 2^2)
Distance = sqrt(16 + 4)
Distance = sqrt(20) km.
Also, sqrt(20) can be simplified as sqrt(4 * 5) = 2*sqrt(5) km.
Both A and C represent the same value.