How to reflect a point off a line with an arbitrary slope

In the workings below I demonstrate (using previous workings) how to reflect a point off a line with an arbitrary slope.

Part 1


Part 2


Part 3


Part 4


Part 5

Part 6


If you'd like evidence that these workings are correct, just visit the Desmos graph: https://www.desmos.com/calculator/tpb3zsca3a

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