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 \(6\)!

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