Why hasn't the distance from this point to the straight line been calculated?

Questions
1

Clear[“Global`*”]

reg = ImplicitRegion[ x + k y == 0, {x, y}]

pt = {-((a^2 k)/Sqrt[b^2 + a^2 k^2]), b^2/Sqrt[b^2 + a^2 k^2]}

RegionDistance[reg, pt]

Use codes above all
Why is it impossible to find the distance from this point to the straight line?

The known condition is: a > b > 0, and the point is in the first quadrant. k<0

2

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]
3

Thank you! This is an alternative method.

4

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?

5

Give up on ImplicitRegion:

reg = InfiniteLine[{x, y} /.
    Solve[a x + b y + c == 0, y][[1]] /.
   {{x -> 0}, {x -> 1}}]
RegionDistance[reg,
 {x0, y0}]