A luxury yacht starts from the port and sails 35 miles West, then it turns North and sails 10 miles, then it turns East and sails 20 miles, then it turns to its right and sails 10 miles. Where is it with respect to the port from where it started?
- A55 miles West
- B15 miles West
- C15 miles East
- D55 miles East
Solution & Step-by-step Explanation
Let's trace the path of the yacht step-by-step starting from the origin (0,0):
Sails 35 miles West: Position becomes (−35,0).
Turns North and sails 10 miles: Position becomes (−35,10).
Turns East and sails 20 miles: Position becomes (−35+20,10)=(−15,10).
Turns right (which is South) and sails 10 miles: Position becomes (−15,10−10)=(−15,0).
Final coordinates are (−15,0), which means the yacht is 15 miles West from the starting port.
Sails 35 miles West: Position becomes (−35,0).
Turns North and sails 10 miles: Position becomes (−35,10).
Turns East and sails 20 miles: Position becomes (−35+20,10)=(−15,10).
Turns right (which is South) and sails 10 miles: Position becomes (−15,10−10)=(−15,0).
Final coordinates are (−15,0), which means the yacht is 15 miles West from the starting port.