A boy leaves his house. He travels 5 km towards South, then travels 8 km towards West and further travels 10 km towards South. How far and in which direction is he from his house now?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 17 km, South West
Moves in the same direction add up, and the distance from the house is the straight line joining the house and the end point. Here both southward moves add up, and the westward move is at right angles to them, so the straight line is the hypotenuse of a right triangle.
Total distance towards South: \(5+10=15\) km
Total distance towards West: 8 km
Straight-line distance by Pythagoras’ theorem: \(\sqrt{15^{2}+8^{2}}=\sqrt{225+64}=\sqrt{289}=17\) km
The boy ends up both south and west of his house, so he is 17 km to the South West.