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Square PQRS is tilted 90 degrees anticlockwise direction around the point P, so that points Q, R, S reach the points Q', R', S' respectively. What is the distance covered by the point R if the length of PQ is 2.
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07 Oct 2019, 01:21
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Square PQRS is tilted 90 degrees anticlockwise direction around the point P, so that points Q, R, S reach the points Q', R', S' respectively. What is the distance covered by the point R if the length of PQ is 2.
Since point P is the hinge point we can take point Q either on left side or on right side of P. As square PQRS is rotated anticlockwise with center at point P, radius would be equal to diagonal PR where PR s equal to √2 * side of square.
PR = 2√2
Here R would cover a distance along the length of perimeter of circle with radius 2√2. Since only 90 deg is rotated, point R would cover only one - fourth the length of circle's perimeter.
Perimeter of circle with radius PR = 2 * π * PR = 2π2√2 = 4π√2
Distance covered by point R = \(\frac{1}{4} * 4π√2\) = π√2
Answer C.
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Square PQRS is tilted 90 degrees anticlockwise direction around the po
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Updated on: 08 Oct 2019, 03:46
Quote:
Square PQRS is tilted 90 degrees anti-clockwise direction around the point P, so that points Q, R, S reach the points Q', R', S' respectively. What is the distance covered by the point R if the length of PQ is 2.
A. (π√2)/3 B. (π√2)/2 C. π√2 D. π√3 E. 2π√3
"AROUND POINT P" means that P is the origin; therefore, the diagonal of the square PQRS is the radius, not the diameter!
square PQRS side = 2 square PQRS diagonal = circle's radius r = side√2 = (2)√2 circle's circumference = 2πr = 2π(2)√2 = 4π√2 distance covered by R to R' (90 deg…360/90…1/4) = (1/4)•4π√2 = π√2
Answer (C)
Originally posted by exc4libur on 07 Oct 2019, 05:50.
Last edited by exc4libur on 08 Oct 2019, 03:46, edited 1 time in total.
Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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07 Oct 2019, 11:48
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If we treat it as though it is an a square inscribed within a circle, then we know that the radius of the circle within which a square is inscribed is half the diagonal of the square. So we already know that PQ=2, and the diagonal of the square = length of side x √2 hence diagonal = 2*√2 Radius of the circle = half of the diagonal = √2
Now the distance covered by the square when it is rotated 90degrees = circumference of the circle * 90/360 = 2*π*√2 *90/36 = 2*π*√2 * 1/4 = π*√2 / 2.
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59% (01:50) correct 
