Word Count : 396

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Let the linear fractional transformation (LFT) be [ w = f(z) = \frac{az + b}{cz + d}, \quad ad - bc \neq 0. ] We are given three distinct points (z_1, z_2, z_3) in the extended (z)-plane and three distinct points (w_1, w_2, w_3) in the extended (w)-plane. We need to show there is only one LFT mapping (z_i \mapsto w_i) for (i = 1,2,3). --- Step 1: Use the cross-ratio property A fundamental property of LFTs is that _________ _____ _____ ________ _________ _________ ____ ________ ______ _____ _____ ________.
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