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06 Oct 2019, 21:33
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Difficulty:
45%
(medium)
Question Stats:
65% (02:17) correct
35%
(02:54)
wrong
based on 81
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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.
A. \((\pi * \sqrt{2})/3\)
B. \((\pi * \sqrt{2})/2\)
C. \(\pi \sqrt{2}\)
D. \(\pi \sqrt{3}\)
E. \(2* \pi \sqrt{3}\)
Updated on: 07 Oct 2019, 03:06
Originally posted by CareerGeek on 06 Oct 2019, 22:09.
Last edited by CareerGeek on 07 Oct 2019, 03:06, edited 2 times in total.
Last edited by CareerGeek on 07 Oct 2019, 03:06, edited 2 times in total.
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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 anti-clockwise 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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And square be placed in first quadrant with Q = (2,0), R = (2,2) & S = (0,2)
When square is rotated anti-clockwise 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
Posted from my mobile device
General Discussion
07 Oct 2019, 00:20
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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
Posted from my mobile device
Distance covered by R is 2πr/4
=π√2
OA:C
Posted from my mobile device
