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# In the figure above, square PQRS, initially in position I, has been ro

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Math Expert
Joined: 02 Sep 2009
Posts: 45498
In the figure above, square PQRS, initially in position I, has been ro [#permalink]

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29 Nov 2017, 22:59
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Difficulty:

45% (medium)

Question Stats:

55% (01:13) correct 45% (01:10) wrong based on 32 sessions

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In the figure above, square PQRS, initially in position I, has been rotated about point S to position II. If P2, Q2 and R2 are the second positions of P, Q and R respectively, and if a
side of the square is 1, what is the length of the path followed by P in rotating to P2 ?

(A) π/4
(B) 1
(C) π/2
(D) 2
(E) π

Attachment:

2017-11-30_0950_002.png [ 5.44 KiB | Viewed 514 times ]

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Re: In the figure above, square PQRS, initially in position I, has been ro [#permalink]

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29 Nov 2017, 23:03
C.

The path followed by P is a quarter circle. Hence the length is 2*pi*r/4. Here r=1. Hence pi/2

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Joined: 04 Jan 2015
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Re: In the figure above, square PQRS, initially in position I, has been ro [#permalink]

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30 Nov 2017, 11:44
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Expert's post
Bunuel wrote:

In the figure above, square PQRS, initially in position I, has been rotated about point S to position II. If P2, Q2 and R2 are the second positions of P, Q and R respectively, and if a
side of the square is 1, what is the length of the path followed by P in rotating to P2 ?

(A) π/4
(B) 1
(C) π/2
(D) 2
(E) π

Attachment:
2017-11-30_0950_002.png

This is a question where we need to have the ability to visualize properly.

From the diagram, we can notice that the position of S has not changed.

Thus, if we consider S as the centre and the length SP as the radius of a circle, we can easily say that the length SP was rotated by 90 degrees and hence the trajectory followed by the point P is of an arc of a quarter circle ( a sector of circle with central angle as 90 degrees)

Thus the length of the path = $$\frac{90}{360} * 2πr = \frac{1}{4} * 2 * π * 1 = \frac{π}{2}$$

Therefore the correct answer is Option C.
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Joined: 01 Feb 2017
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Re: In the figure above, square PQRS, initially in position I, has been ro [#permalink]

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04 Dec 2017, 00:33
We can see that the point P is rotated about point S, as the position of point S is unchanged.

Sector of rotation is 90 degrees or 1/4* Circumference= 1/4*2πr= πr/2.

Now, we are given that radius= SP= SP2= 1.

Therefore, Length of rotation= π/2.

Ans C

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Re: In the figure above, square PQRS, initially in position I, has been ro   [#permalink] 04 Dec 2017, 00:33
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# In the figure above, square PQRS, initially in position I, has been ro

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