Where a line going through random point intersects another line at 90 degrees

In these workings I demonstrate how to find the intersection of two lines perpendicular to each other, whereby one line passes through a random point (a, b). The answers are left in their abstract form.

Part 1

Part 2

Part 3
Part 4

Part 5

Here is a free Desmos graph that can be played around with: https://www.desmos.com/calculator/7bmvuhqr3n

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