Starting from a point, Suraj walked 20 m south, then he turned left and walked 18 m, he again turned left and walked 18 m, then he turned right and walked 10 m. How far and in which direction is he now from the starting point?
- A784
m in north - B788
m in south-east - C786
m in south-west - D790
m in north-west
Solution & Step-by-step Explanation
Let's trace Suraj's movements coordinate-wise starting from (0,0):
Walks 20 m South: Coordinates become (0,−20).
Turns left (East) and walks 18 m: Coordinates become (18,−20).
Turns left (North) and walks 18 m: Coordinates become (18,−20+18)=(18,−2).
Turns right (East) and walks 10 m: Coordinates become (18+10,−2)=(28,−2).
Now, let's find his straight-line distance from the starting point (0,0):
Distance=
28
2
+(−2)
2
=
784+4
=
788
m
Since his coordinates are (28,−2) (positive x, negative y), he is located in the South-East direction.
Walks 20 m South: Coordinates become (0,−20).
Turns left (East) and walks 18 m: Coordinates become (18,−20).
Turns left (North) and walks 18 m: Coordinates become (18,−20+18)=(18,−2).
Turns right (East) and walks 10 m: Coordinates become (18+10,−2)=(28,−2).
Now, let's find his straight-line distance from the starting point (0,0):
Distance=
28
2
+(−2)
2
=
784+4
=
788
m
Since his coordinates are (28,−2) (positive x, negative y), he is located in the South-East direction.