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Re: Coordinate System and Geometry [#permalink]
19 Nov 2012, 22:30

Expert's post

are you sure about \(\sqrt{3}\) as the answer. As per my calculations i got \(\sqrt{2}\) as the answer. If I am correct, then I will surely post my answer. _________________

Re: Coordinate System and Geometry [#permalink]
19 Nov 2012, 22:47

Expert's post

Step 1: Measure the radius. That will come out to be 2. Step 2: Observe the diagram. Since both OP and OQ are the radii, their measure will be 2 only. Step 3: Draw a line parallel to x axis, from P to Q. Step 4: Angle OQP and angle OPQ= 45 In the diagram attached, the angles marked X are 45 and 45 degrees. Step 5: Draw a perpendicular from Q to x axis. The point at which it meets the X axis, mark it as A. Step 5: The triangle OPA is a 45:45: 90 degree tiangle. This triangle has the property that the hypotenuese:side 1:side 2 will be in the ration \(\sqrt{2}\):1:1. Step 6: Since side 1(OA) and side 2(AQ) are equal, therefore let them be x. These will be equal to \(2/\sqrt{2}\). Step 7: The length of side 1 will come out to be \(2/\sqrt{2}\) or simply \(\sqrt{2}\).

Please let me know what my mistake, if my solution is wrong.

Re: Coordinate System and Geometry [#permalink]
19 Nov 2012, 23:51

Marcab wrote:

Step 1: Measure the radius. That will come out to be 2. Step 2: Observe the diagram. Since both OP and OQ are the radii, their measure will be 2 only. Step 3: Draw a line parallel to x axis, from P to Q. Step 4: Angle OQP and angle OPQ= 45 In the diagram attached, the angles marked X are 45 and 45 degrees. Step 5: Draw a perpendicular from Q to x axis. The point at which it meets the X axis, mark it as A. Step 5: The triangle OPA is a 45:45: 90 degree tiangle. This triangle has the property that the hypotenuese:side 1:side 2 will be in the ration \(\sqrt{2}\):1:1. Step 6: Since side 1(OA) and side 2(AQ) are equal, therefore let them be x. These will be equal to \(2/\sqrt{2}\). Step 7: The length of side 1 will come out to be \(2/\sqrt{2}\) or simply \(\sqrt{2}\).

Please let me know what my mistake, if my solution is wrong.

your solution is wrong in Step 3. PQ is parallel to x axis is an assumption in the solution and has not been stated in question. Figures are not drawn to scale. _________________

Re: Plane Geometry, Semicircle from GMATPrep [#permalink]
10 Dec 2013, 05:34

Bunuel wrote:

zz0vlb wrote:

I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.

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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\); Point P in II quadrant \((-\sqrt{3}, 1)\); Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP); Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).

Is it the case of reflection in Y axis ? I doubt that but still want to clarify..

Re: Plane Geometry, Semicircle from GMATPrep [#permalink]
10 Dec 2013, 05:40

Expert's post

ygdrasil24 wrote:

Bunuel wrote:

zz0vlb wrote:

I need someone like Bunuel or walker to look at my statement and tell if this is true.

Since OP and OQ are perpendicular to each other and since OP=OQ=2(radius) , the coordinates of Q are same as P but in REVERSE order, keep the sign +/- based on Quandrant it lies. in this case Q(1,\sqrt{3)}.

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

Yes you are right.

Point Q in I quadrant \((1, \sqrt{3})\); Point P in II quadrant \((-\sqrt{3}, 1)\); Point T in III quadrant \((-1, -\sqrt{3})\) (OT perpendicular to OP); Point R in IV quadrant \((\sqrt{3},-1)\) (OR perpendicular to OQ).

Is it the case of reflection in Y axis ? I doubt that but still want to clarify..

No. \((-\sqrt{3}, 1)\) is not a reflection of \((1, \sqrt{3})\) around the Y-axis. The reflection of \((1, \sqrt{3})\) around the Y-axis is \((-1, \sqrt{3})\). _________________

Re: In the figure above, points P and Q lie on the circle with [#permalink]
11 Dec 2013, 11:51

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

This problem took be a bit to conceptualize but I got it as soon as I realized that the graph I was looking at wasn't drawn completely accurately.

If you are to accurately graph the point -√3,1 on a piece of graph paper, you see that the angle it forms with regards to the origin (and the x plane) is less than 45 degrees. Because of this, and the fact that both points lie on the circle, and that the two radii form a 90 degree angle, Q must be higher on the circle than P. Upon looking at this graph, I thought that the x and y coordinates of Q would be the same (except positive) which is, I am sure, the intent of the test makers. The answer is simply the positive reciprocal of point P.

Re: In the figure above, points P and Q lie on the circle with [#permalink]
12 Dec 2014, 22:19

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