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UV projection for fixed function reflection

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I'm doing a DirectX9 fixed function project and needing to calculate a texture matrix for transforming a plane with uv'x from (0, 0) to (1, 1) to the projected uvs from a reflection.
At the moment I am able to get individual projected points, iv read that with 3 points I would be able to construct the required matrix, but can not find anywhere that states the steps to get the matrix.

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