O is the origin of the coordinate system above, and A lies in the 2nd

Question

https://gmatclub.com/forum/download/file.php?id=62037 O is the origin of the coordinate system above, and A lies in the 2nd quadrant. If angle OAB is a right angle, what are the coordinates of point A? (1) The length of line segment OA is 5. (2) The length of line segment AB is 5. 1.png

ramlala · Answer

https://gmatclub.com/forum/download/file.php?id=62037 
O is the origin of the coordinate system above, and A lies in the 2nd quadrant. If angle OAB is a right angle, what are the coordinates of point A?

(1) The length of line segment OA is 5. 
We do not know AB or any of the other angle.

Insufficient

(2) The length of line segment AB is 5.
We do not know OA or any of the other angle.

Insufficient

Statement 1 & 2
As OA=AB=5 we can get OB.

Sufficient

C

Jazzutds · Answer

I think the answer is E. You need to know the slope of one of the lines to determine the coordinate of A

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the27s · Answer

C it should be.

Knowing just the one side and one included angle isn't sufficient to determine A - Angles made by OA and AB with y-axis are unknown.

Combining both gives right isosceles triangle, implying the angles made with y-axis would be 45 deg., extending to angles made with X-axis will also be 45deg.

With the above information known, determining A co-ordinates is fairly straightforward and doesn't need computation.

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SiddharthR · Answer

The answer is "C"

Lets assume A has the coordinate (x,y) B has the coordinate (0,B) (x coordinate is 0 since B is on Y axis) and O is origin (0,0)

Statement I) Using distance formula, we have x^2 + y^2 = 25 (Multiple combination solutions of x & y). Insufficient
Statement II) Same as above using distance formula we have (x^2 + (y - b)^2) = 25. Insufficient

When you combine both statements, you have (x^2 + (y - b)^2) = x^2 + y^2

Solving this results in b(b - 2y) = 0; b coordinate cannot be 0 here since then we won't have a triangle and B coordinate is at the origin. Instead, b - 2y = 0 --> b = 2y

Also, from combining both statements we know that OB = 5sqrt(2) (b coordinate) because we have a right triangle with two sides given, so the hypotenuse is the sqrt of the sum of squares of the other two sides.

OB is nothing but coordinate 'b' of point B. Therefore we have 2y = 5sqrt(2). We can solve for y

Now we have y, we can solve for x by using x^2 + y^2 = 25 in statement I

O is the origin of the coordinate system above, and A lies in the 2nd

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O is the origin of the coordinate system above, and A lies in the 2nd

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