For any point (x, y), √(x² + y²) = the distance between (x, y) and the origin.
W = (a, b)
X = (c, d)
Since we are told that a² + b² = c² + d², we get:
√(a² + b²) = √(c² + d)
(distance between W and the origin) = (distance between X and the origin).
The same reasoning can be applied to Y and Z.
Thus:
(distance between Y and the origin) = (distance between Z and the origin).
Question: What is XZ - WY?
XZ = (distance between X and the origin) + (distance between Z and the origin)
WY = (distance between W and the origin) + (distance between Y and the origin)
Since the values in red are equal and the values in blue are equal, XZ = WY.
Thus:
XZ - WY = 0.
The correct answer is C.
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