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# PS Co-ordinate Geo (Warning: GMATPrep)

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Manager
Joined: 02 Jan 2007
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PS Co-ordinate Geo (Warning: GMATPrep) [#permalink]  24 Apr 2007, 14:11
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Somebody please tell me that GMATPrep lost its mind and the OA isn't B
I thought OQ was the mirror-image of OP
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Current Student
Joined: 22 Apr 2007
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They are just trying to trick you into thinking that OQ is mirror image of OP by making it look like that in the picture. There's no mathematical reason for you to believe so.

Now, imagine the angle formed by negative X axis, O and P as <w

From the location of P, we can infer that

r Cos w = (3)^1/2, and
r Sin w = 1

Now, imagine the angle formed by P, O and positive Y axis is <k

So, w + k = 90 degrees

Now, imagine the angle formed by Q, O and the positive Y axis is <h

t = r Cos h
s = r Sin h

we know that k + h = 90
So, w = h

So,

t = r Cos w
s = r Sin w

From earlier, we know that r Sin w = 1
So, s = 1
Manager
Joined: 02 Jan 2007
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Is there a way to get to the OA without using trignometry
I dont know trignometry did some 10 years back in school but I'm blank now.

OP = 2 so OQ =2 and
OPQ would make an isosceles triangle
so PQ = 2sqrt(2)
so if we add we get
-sqrt(3) + 2sqrt(2) = -1.7 + 2(1.4) = 1.1

Intern
Joined: 08 May 2006
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Here's how I did it:
The two lines are perpendicular => they have inverse negative slope of each other -1/sqrt3 and sqrt3.

We know (t-0)/(s-0) = sqrt 3 (from slope formula using line to the origin)
=> t =(sqrt3)s
and t^2 +s^2 = 4 (length of the radius)

=> t^2 +3t^2 = 4

t = 1
Manager
Joined: 02 Jan 2007
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Thanks doc. Slope didnt strike me. Nice idea.
Intern
Joined: 26 Feb 2007
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What do you guys think of this method.
Use pythagorean theorem to find that the left hypotenuse is =2. This is also the radius.

Since its a 1, sqrt(3), 2 triangle then the angles are 30,60, 90.

So the angle next to the 90degree has to be 30deg. Therefore the angle at the right side has to be 60.

now if you look at the right side you now have a 30,60,90 triangle and the hypotenuse is 2 and therefore x has to equal 1.

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