How to find the distance from this point to a straight line?

Asked Aug 28 '23 at 23:42

Active Aug 30 '23 at 06:40

Viewed 146 times

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]

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

the right answer is:

Clear["Global`*"] 
reg = ImplicitRegion[a x + b y + c == 0, {x, y}] 
pt = {x0, y0}
RegionDistance[reg, pt]

Why can't the distance formula from a point to a straight line be derived using code?

edited Aug 30 '23 at 06:40

asked Aug 28 '23 at 23:42

csn899

2

I wouldn't expect RegionDistance to work with undefined terms (e.g. a, b, k). – lericr Aug 29 '23 at 00:01
Is there any other way to calculate? – csn899 Aug 29 '23 at 00:04
4

@lericr But it does: RegionDistance[ImplicitRegion[x + k y == 0, {x, y}], {p1, p2}] – xzczd Aug 29 '23 at 00:12
4

You seem to ignore the error message....Why is that? – Michael E2 Aug 29 '23 at 00:12
2

“Why is it impossible to find the distance from this point to the straight line?” No, it's possible, if you think a bit more. – xzczd Aug 29 '23 at 00:34
@xzczd Which part needs to be modified? – csn899 Aug 29 '23 at 03:43
The answer is already there, think carefully. – xzczd Aug 29 '23 at 04:17
2

Simplify[ RegionDistance[reg, {p1, p2}] /. Thread[{p1, p2} -> pt], {a > b > 0, k < 0}] – cvgmt Aug 30 '23 at 01:08
@cvgmt Clear["Global`*"] reg = ImplicitRegion[a x + b y + c == 0, {x, y}] pt = {x0, y0} RegionDistance[reg, pt]Why can't the distance formula from a point to a straight line be derived using code? – csn899 Aug 30 '23 at 06:39

0 Answers0