Question 1
A man starts from point A and walks 10 km East to point B. He then turns North and walks 3 km to point C. He then turns West and walks 14 km to point D. Finally, he turns South and walks 6 km to point E. How far and in which direction is he from his starting point A?
Answer and explanation
Correct answer: A
Let the starting point A be (0,0).
Point B is 10 km East, so B = (10, 0).
Point C is 3 km North from B, so C = (10, 3).
Point D is 14 km West from C, so D = (10 - 14, 3) = (-4, 3).
Point E is 6 km South from D, so E = (-4, 3 - 6) = (-4, -3).
The final position E is 4 km West and 3 km South of the starting point A.
The distance from A to E is the hypotenuse of a right-angled triangle with sides 4 km and 3 km.
Distance = √(4² + 3²) = √(16 + 9) = √25 = 5 km.
The direction is South-West.
