Neha starts from Point A and drives 11 km towards the east. She then takes a right turn, drives 8 km, turns right and drives 14 km. She then takes a right turn and drives 12 km. She takes a final right turn, drives 3 km and stops at Point P. How far (shortest distance) and towards which direction should she drive in order to reach Point A again? (All turns are 90-degree turns only unless specified.)
4 km to the south
Place A at the origin \((0, 0)\) with east as \(+x\) and north as \(+y\).
Drive 11 km east: reach \((11, 0)\).
Right turn now faces south; drive 8 km: reach \((11, -8)\).
Right turn now faces west; drive 14 km: reach \((11 - 14, -8) = (-3, -8)\).
Right turn now faces north; drive 12 km: reach \((-3, -8 + 12) = (-3, 4)\).
Right turn now faces east; drive 3 km: reach \((-3 + 3, 4) = (0, 4)\), which is Point P.
P is at \((0, 4)\) and A is at \((0, 0)\); they share the same \(x\), so P is 4 km due north of A.
Therefore Neha must drive 4 km to the south to reach Point A again.
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Important Questions from Direction and Distance
What is the direction of U with respect to P?
What is the shortest distance between R and T?
If a person walks 3m towards the North from point V, takes a right turn and walks for another 15m, which of the following points would he reach?
In which direction is Amit facing at point F?
What is the distance between the starting point and the end point?
