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Coordinate Geometry question

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by Spartacus2000 » Tue Aug 09, 2011 6:16 pm
Image

In the attached figure, points P and Q lie on the circle with center O. what is the value of s?

(1) 1/2
(2) 1
(3) Root 2 (could not find the symbol for root)
(4) Root 3
(5) Root 2/2

Img. is attached - I hope it is displayed

Thanks.[/img]

Just realized this is in the wrong section, sorry about that.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Aug 09, 2011 9:13 pm
Spartacus2000 wrote:Image

In the attached figure, points P and Q lie on the circle with center O. what is the value of s?

(1) 1/2
(2) 1
(3) Root 2 (could not find the symbol for root)
(4) Root 3
(5) Root 2/2

Img. is attached - I hope it is displayed

Thanks.[/img]

Just realized this is in the wrong section, sorry about that.
Coordinates of point O, the origin are (0, 0)
Angle POQ = 90º, so the slope of OP * slope of OQ = -1 (the product of the slopes of two perpendicular lines is -1).
We can find the slope of OP, as we know their coordinates.
Slope of OP = (1- 0)/(-√3 - 0) = -1/√3
So, slope of OQ = √3/1 or (√3 - 0)/(1 - 0), which implies the x-coordinate of point Q is 1 or s = 1.

The correct answer is B.
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by gmatboost » Tue Aug 09, 2011 10:38 pm
Here is a step-by-step description solving this question.

https://www.beatthegmat.com/circle-i-can ... tml#393687
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by GMATGuruNY » Wed Aug 10, 2011 2:21 am
I posted an illustrated solution here:

https://www.beatthegmat.com/gmatprep-q-x ... tml#394684
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