Moksh starts from Point A and drives 21 km towards the south. He then takes a left turn, drives 14 km, turns left and drives 29 km. He then takes a left turn and drives 21 km. He takes a final left turn, drives 8 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90-degree turns only unless specified.)
7 km to the east
Take A as the origin and track east (x) and north (y) coordinates. Start at A = (0, 0).
Drive 21 km south: position (0, −21), facing south.
Left turn faces east; drive 14 km: position (14, −21).
Left turn faces north; drive 29 km: position (14, 8).
Left turn faces west; drive 21 km: position (14 − 21, 8) = (−7, 8).
Left turn faces south; drive 8 km: position (−7, 8 − 8) = (−7, 0). This is Point P.
A is at (0, 0) and P is at (−7, 0). To go from P to A, x must increase from −7 to 0, a distance of 7 km towards the east, with no change in the north-south direction.
Hence, Moksh should drive 7 km to the east to reach Point A.
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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?
