Points X, Y, and Z are located on the rectangular coordinate

Well of course you can use the distance formula but do realize that the distance formula is not really covered by the Original Guide. Hence, they had to provide a 3rd coordinate to make it a right angled triangle so that you could use the pythagorus theorem. Using the distance formula:

For 2 points: A & B, Distance between A and B \(=\sqrt{({(x_1-x_2)}^2 + {(y_1-y_2)}^2)}\)
Where \(A=(x_1,y_1)\) & \(B=(x_2,y_2)\)

In the question above \(Y=(-4,3)\) & \(Z=(2,-3)\)
Distance between 2 points, Y & Z, on the coordinate system \(=\sqrt{({(-4-2)}^2 + {(3+3)}^2)}\)

Which is \(=\sqrt{(6^2 + 6^2)}\)
Which is \(=\sqrt{72}\)
Which is \(=6\sqrt{2}\)

So Yes, to answer your question, info about \(Y\) & \(Z\) alone is sufficient "if you know the formula for deriving the distance between two coordinates", but otherwise you need to know a third point to first establish it is a right angled triangle. Works either ways. I have seen numerous statistics questions where GMAT actually gives you the formula for calculating the sum of the series, even though we need to know it to solve quite a few question on the GMAT. Either ways, your pick. Answer still remains the same \(=6\sqrt{2}\) and not \(6\)!