Prep- Geometry

Actually there is a theorem in Geometry (don't know really exist or not but I have proved it myself, didn't bother to search it on net).

You can check the link to view more on this: https://www.beatthegmat.com/coordinate-s ... 12489.html

Concept: The distance between two point will we same on interchanging the values of x-coordinate and y-coordinate of a point and keeping fixed the other point.

Your question is somewhat same and near to this concept; only the thing is the it is asked in reverse order.

Since both PO and QO are radii of circle, therefore distance would be same. Now if the distance is same we are using (0, 0) as the center or intersecting point for both lines then we can easily swap the coordinates.

So, it means you need not to do any calculation at all, just swap the coordinates and reverse the sign as it in upper half of the coordinate system.

Hope it helps....

please do search appropriately before posting a new question, it unnecessarily takes the space and time of lot of posters.

the question has been answered before..

thanks

Here is the proof in a nutshell:

You have two isoceles right triangles after drawing an imaginary line through P and Q.

The two new triangles are
(0,0), (-sqrt(3),1) and (1,0)
and
(0,0), (s,t) and (1,0)

The length of one side of the triangle is 1. The hypotenuese is sqrt 3.

Therefore the length of the other side is 1.

S, therefore, is equal to 1 .

You cannot assume you will have two isoceles triangles after the imaginary line draw between the points, if this were the case then for the triangle on the left, you would not have two known sides of radical 3 and 1, using the theory of Pythagorus, we know that the length of the hypotenuse for the left triangle formed after drawing a line connecting the two points is 2.

Because all radii are equal, the other radii must be 2 as well, using the theorem again, we find that the connecting line must be equal to radical 8, simplified to 2 radical 2.

Now given that from point P to the y axis is radical 3, we solve for what is needed to be added to radical 3 to equate to 2 radical 2, in decimal form, for accuracy, we find that radical 3 (1.73205) plus X = 2 radical 2 (2.82842), solve for X, X=1.0963, or ~1.

DO NOT assume two isoceles triangles are formed, just because it works out once, does not hold true always.

agemroy wrote:


Shouldnt the answer be sqrt(2)?? How is it 1?

Here is a two step solution to this problem.

We know from the figure that angle formed at the origin is 90.

Therefore, PQ is perpendicular on ST

Slope of line from orgin to point PQ is -1/sqrt3

Hence slope of line from origin to ST is sqrt3/1

Therefore point S is 1.

Let me know if you have any doubts.

Hey,

That was helpful. Dont know how i missed out the slope concept?

Thanks