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Sita starts from point P, walks 10 km towards East, turns right and walks 8 km, then turns right and walks 4 km. How far (shortest distance) is she from the starting point P?
10 km
12 km
8 km
6 km
10 km
Represent the path as a right-angled triangle by finding horizontal and vertical net displacement: (10тБ╗тБ┤) horizontal and 8 vertical.
Represent the path as a right-angled triangle by finding horizontal and vertical net displacement: (10тБ╗тБ┤) horizontal and 8 vertical.
Coordinate Mapping
Starting at P(0,0), she walks 10km East to (10,0). She turns right (South) and walks 8km to (10,-8). She turns right (West) and walks 4km to reach (6,-8).
Calculate Displacement
The horizontal distance from P is (10тИТ4) = 6 km. The vertical distance from P is 8 km. Shortest distance = square root of (6┬▓ + 8┬▓) = square root of (36 + 64) = square root of 100 = 10 km.
B: 12 km is incorrect as it does not follow the Pythagorean displacement calculation. C: 8 km ignores the horizontal shift. D: 6 km represents only the net horizontal shift, not the total hypotenuse.
A is correct because the resultant displacement based on the Pythagorean theorem (root of 6 squared plus 8 squared) yields exactly 10 km.
Always convert direction problems into X-Y coordinate planes to avoid visual confusion; the shortest distance is always the hypotenuse of the resulting displacement triangle.