If I assume that “PQ” is a line sigment then I get correct answer, but since it’s not given, there is a possibility that “PO” is a line segment and “OQ” is another line segment and in that case the answer becomes “d”. How to handle these kind of cases ?
Ideally, the question would have some clarity if asked in the GRE.
Otherwise, you can consider the point marked at O simply just the origin point.
It’s visually collinear, so i’m not sure why you’d consider them not collinear. Also, there would be no point for that question because nothing would be tested if they weren’t collinear, since, as you noted, a and b can be anything.
Also, based on this, it’s seems somewhat clear that they would distinguish between the two lines if they were actually distinct.
So, if not given explicitly that “O” is a endpoint, I should assume that it is not.
Reason I’m clarifying this is that I’ve seen multiple question where visually the two distances may look equal or point may look like center of circle but If I assume that, I get incorrect answer. So, I’m trying to generalize a way by which I can distinguish when to assume and when to not.
If points A, B, and C all lie on a single straight line, then they are collinear. It would be silly for them to claim that what is clearly one straight line is actually two line segments.
Additionally, this is coordinate geometry, where everything is to scale anyway.