A girl starts from a point P and walks 10 metres in the north-west direction and reaches the point Q. She then turns to her left and walks 10 metres to a point R, which is directly westward of point P. She again moves towards the south-east direction and goes 10 metres and reaches a point S, which is directly southward of point Q. From point S she turns towards point P and walks 10 metres. What is the shape of the geometrical figure PQRS?
ARhombus
BRectangle
CSquare ✓ Correct
DParallelogram
Correct answer: (C) Square
Explanation
PQRS is a square.
Place P at (0,0); Q is 10 m north-west at about (-7.07, 7.07).
A left turn heads south-west; R = (-14.14, 0), due west of P.
R to south-east 10 m gives S = (-7.07, -7.07), due south of Q.
All four sides are 10 m and PQ is perpendicular to QR, so all angles are 90 degrees.
Equal sides with right angles make it a square.
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