Is this the complete question ?

Because if a triangle is created in Quadrant 4 , all x > y , and in 1st qudrant 50/50 chances for x > y .. In this 2nd quadrant its 0 probability , Its 50 /50 again if triangle is in 3rd quadrant .
If a traingale always lives within one quadrant , then probability would vary as i explained.

But if a triangle spans across various quadrants its important to know how it co-ordinates would be like . So it can vary dedepnding on more information .

If instead of triangle we would have a circle ,lets say, with centre at origin (0,0) then answer to your question for x> y would be 4/8 = 1/2....

Some body may want to help here