Coordinate Geometry

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Coordinate Geometry

by amirhakimi » Wed Nov 06, 2013 8:30 pm
In the figure shown, points P and Q lie on the circle with center O. What is the value of S?

A) 1/2
B) 1
C)sqrt(2)
D)sqrt(3)
E)[sqrt(2)]/2

Answer is B
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by amirhakimi » Wed Nov 06, 2013 8:32 pm
Aren't P and Q symmetry upon y-axis?

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by theCodeToGMAT » Wed Nov 06, 2013 9:31 pm
Answer {B}
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by theCodeToGMAT » Wed Nov 06, 2013 9:37 pm
amirhakimi wrote:Aren't P and Q symmetry upon y-axis?
The solution to this problem lies in the concept of 30-60-90 triangle.
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by mevicks » Wed Nov 06, 2013 10:00 pm
Image
In the figure shown, points P and Q lie on the circle with center O. What is the value of s?
(A) 1/2
(B) 1
(C) √2
(D) √3
(E) 1/√2
10 Secs Approach:
Rotate the figure at point O
Image
Q has the coordinates [spoiler](1, √3) and s = 1; answer B[/spoiler]

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by mevicks » Wed Nov 06, 2013 10:00 pm
amirhakimi wrote:Aren't P and Q symmetry upon y-axis?
Nope they are not symmetric. We should not rely on the GMAT to provide us figures drawn to scale (implying you cannot use a protractor to measure their diagrams :D )

Image
In the figure shown, points P and Q lie on the circle with center O. What is the value of s?
(A) 1/2
(B) 1
(C) √2
(D) √3
(E) 1/√2

Consider the above problem again:
In ∆PAO, the sides are 1, √3, and 2. Thus it is a 30-60-90 triangle as shown.
Image

Complete the other angles and drop a perpendicular to B. It is our new 30-60-90 triangle.
The sides are again 1, √3, and 2.
Image

thus Q has the co-ordinates (s,t) = [spoiler](1, √3) and s = 1[/spoiler]

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by [email protected] » Thu Nov 07, 2013 12:36 am
Hi amirhakimi,

Since other posters have properly explained the "math" behind this question, I won't rehash it here.

I do want to reiterate certain tactics that you'll find useful in these types of questions:

1) ANY diagonal line on a graph can be determined by drawing a right triangle "around it." This is a useful tactic on most questions involving graphs.

2) The GMAT regularly tests certain right triangles (30/60/90, 45/45/90, 3/4/5, 5/12/13), so be on the look out for those triangles.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by amirhakimi » Thu Nov 07, 2013 12:44 am
That was the the first principal of MGMAT on Geometry and I completely forget about that.
"DON'T ASSUME WHAT YOU DON'T KNOW FOR SURE!"
Getting this answer wrong was my punishment for not paying attention to principals :D
Thanks for the heads-up my friend :)
mevicks wrote: Nope they are not symmetric. We should not rely on the GMAT to provide us figures drawn to scale (implying you cannot use a protractor to measure their diagrams :D )