Diagram determines whether question is solvable (1 Viewer)

[QZP]

Q: "If O,A,P,Q respectively represent complex numbers 0, 1, z1, z2, construct the point R so that △OAP is similar to △ORQ. Find the complex number represented by R.
A: R = z1/z2.

Now, consider arg(R) = arg z1 - arg z2

My diagram:

Notice how this will result in arg(r) = arg z1 + arg z2 which means I cannot reach the answer

But in this diagram:

This will result in arg (r) = arg z1 - arg z2 which is what is required for the answer

So how do I know how to draw the "correct" diagram from the start?

Edit: There are questions after which I cannot do because I don't know how the diagram is meant to be orientated -_-

 

[seanieg89]

Well the question is misleading with the line "Find the complex number represented by R".

As you have pointed out, there are two choices because if we reflect a triangle about one of its sides we get a similar triangle (in fact congruent), although it's orientation is reversed.

If this ambiguity persists in other questions, they probably mean "similar and similarly oriented" when they say "similar".

*Note that if triangle ABC is similar to triangle XYZ, we say that the two triangles are similarly oriented if tracing out ABC and XYZ is either clockwise or counterclockwise for both of them.

 

[QZP]

Thanks! That helped a lot