Read the following information to answer the given question. Starting from…

2024

Read the following information to answer the given question.

Starting from point A, Jackie Chan walked 50 m towards the west. He turned left and walked 20 m and did a somersault.

He then turned left and walked 50 m and did a backflip. After this, he turned to his right and walked 10 m. How far and in which direction is Jackie Chan from A?

  1. A.

    30 m, South

  2. B.

    30 m, North

  3. C.

    40 m, South

  4. D.

    40 m, North

Show answer & explanation

Correct answer: A

Concept: In direction-sense problems, resolve the path into net displacement along two perpendicular axes — East-West and North-South — rather than adding the raw path length. A left turn rotates the facing direction 90° counter-clockwise (North → West → South → East → North), and a right turn rotates it 90° clockwise (North → East → South → West → North). When two legs on the same axis are equal and opposite, they cancel completely, so the remaining legs on the other axis add directly to give the straight-line distance from the start.

Application:

  1. Start at A, facing west. Walk 50 m west to reach B (net so far: 50 m west of A).

  2. At B, turn left: facing west, a left turn points south. Walk 20 m south to reach C (net: 50 m west, 20 m south of A).

  3. At C, turn left again: facing south, a left turn points east. Walk 50 m east to reach D — this exactly cancels the earlier 50 m west leg, so D lies directly south of A, 20 m south.

  4. At D, turn right: facing east, a right turn points south. Walk 10 m south to reach E. D and E both lie on the same north-south line through A, so the southward legs add: 20 m + 10 m = 30 m south of A.

Cross-check (coordinates, east = +x, north = +y, A = (0, 0)): B = (-50, 0) after the west leg; C = (-50, -20) after the south leg; D = (0, -20) after the east leg — D shares A's x-coordinate, matching the diagram's dashed vertical line through A and D; E = (0, -30) after the final south leg. The straight-line distance from A(0, 0) to E(0, -30) is 30 m due south, confirming the option "30 m, South".

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