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

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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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