Give up on ImplicitRegion:
ImplicitRegion
reg = InfiniteLine[{x, y} /. Solve[a x + b y + c == 0, y][[1]] /. {{x -> 0}, {x -> 1}}] RegionDistance[reg, {x0, y0}]
I don't know, but this variant works correctly:
reg = InfiniteLine[{{0, 0}, {-k, 1}}]; pt = {-((a^2 k)/Sqrt[b^2 + a^2 k^2]), b^2/Sqrt[b^2 + a^2 k^2]}; RegionDistance[reg, pt]
Using this code to derive the distance from a point to a straight line is also unsuccessful.
Clear["Global`*"]
reg = ImplicitRegion[a x + b y + c == 0, {x, y}]
pt = {x0, y0}
RegionDistance[reg, pt]
Is there any method to derive the distance formula from a point to a straight line?
