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Square PQRS is tilted 90 degrees anticlockwise direction around the po
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06 Oct 2019, 21:33
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Competition Mode Question 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. A. \((\pi * \sqrt{2})/3\) B. \((\pi * \sqrt{2})/2\) C. \(\pi \sqrt{2}\) D. \(\pi \sqrt{3}\) E. \(2* \pi \sqrt{3}\)
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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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Updated on: 07 Oct 2019, 03:06
Let the point P be origin. And square be placed in first quadrant with Q = (2,0), R = (2,2) & S = (0,2)
When square is rotated anticlockwise 90 deg, point R travels along the arc of the circle of radius PR = \(\sqrt{2}\)
The new coordinates are P(0,0), Q’(0,2), R’(2,2), S’(2,0)
Distance travelled by point R is nothing but the length of the arc RR’ of circle with radius PR and angle 90 deg at the center
—> RR’ = θ/360*2*π*r = 90/360*2*π*\(\sqrt{2}\) = π*\(\sqrt{2}\)
IMO Option C
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Originally posted by Dillesh4096 on 06 Oct 2019, 22:09.
Last edited by Dillesh4096 on 07 Oct 2019, 03:06, edited 2 times in total.



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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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07 Oct 2019, 00:20
If we consider a circular in which square is inscribed,Radius of the circle will be 2√2
Distance covered by R is 2πr/4
=π√2
OA:C
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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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07 Oct 2019, 01:21
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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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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07 Oct 2019, 04:36
Please, Find The Attached 90º Rotation anticlockwise direction around the point P is inscribed in a circle.
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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 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.
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.



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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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07 Oct 2019, 11:48
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.
The answer is therefore B.



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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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07 Oct 2019, 12:20
We can calculate the r =2sqrt2 and then we can calculate the area of the arc in the sector
The answer should be C.



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Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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08 Oct 2019, 03:28
Dillesh4096 wrote: —> RR’ = θ/360*2*π*r = 90/360*2*π*\(\sqrt{2}\) = π*\(\sqrt{2}\)
your calculation is wrong: 90/360*2*π*\(\sqrt{2}\)… 1/4*2*π*\(\sqrt{2}\)… 1/2*π*\(\sqrt{2}\)… π*\(\sqrt{2}\)/2…




Re: Square PQRS is tilted 90 degrees anticlockwise direction around the po
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08 Oct 2019, 03:28






