Hi gmat_thingie,

Before we deal with the specifics of this DS question, it's important to note that in a DS prompt, the picture is NOT necessarily drawn to scale, so we cannot tell, just by looking at the picture, if (-1, -1) is on the line or not.

We're asked if (-1, -1) is on line OQ. This is a YES/NO question.

Fact 1: Point P = (-2, 2)

Unfortunately, this does not tell us anything about line OQ, so there's no way to determine if (-1, -1) is on line OQ or not.
Fact 1 is INSUFFICIENT

Fact 2: Angle POQ = 90 degrees

This tells us 1 thing about lines OP and OQ: since the lines cross at a 90 degree angle, the two lines are perpendicular. This also means that the two lines have an "opposite inverse" set of slopes. However, this is not enough to determine if (-1, -1) is on line OQ or not.
Fact 2 is INSUFFICIENT

Combined, we know....
1) Two points on line OP: (0,0) and (-2, 2); with this, we can determine the slope of line OP - it's slope is -1.
2) Angle POQ = 90 degrees, so the slope of line OQ is 1 (it's the opposite inverse of -1).
3) Point (0,0) is also on line OQ, so with a slope of 1, we can form the equation Y = 1X. The point (-1, -1) is another solution to this equation, so we now have PROOF that it is on line OQ
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich