diff --git a/docs/src/lib/sets/EmptySet.md b/docs/src/lib/sets/EmptySet.md
index 8fc5630ff7..f41c73091a 100644
--- a/docs/src/lib/sets/EmptySet.md
+++ b/docs/src/lib/sets/EmptySet.md
@@ -77,6 +77,7 @@ Undocumented implementations:
 * [`vertices_list`](@ref vertices_list(::LazySet))
 * [`vertices`](@ref vertices(::LazySet))
 * [`volume`](@ref volume(::LazySet))
+* [`distance`](@ref distance(::AbstractVector, ::LazySet))
 * [`exponential_map`](@ref exponential_map(::AbstractMatrix, ::LazySet))
 * [`∈`](@ref ∈(::AbstractVector, ::LazySet))
 * [`is_interior_point`](@ref is_interior_point(::AbstractVector, ::LazySet))
diff --git a/src/Sets/EmptySet/EmptySetModule.jl b/src/Sets/EmptySet/EmptySetModule.jl
index 491b70bcbf..bbe9e228a0 100644
--- a/src/Sets/EmptySet/EmptySetModule.jl
+++ b/src/Sets/EmptySet/EmptySetModule.jl
@@ -4,6 +4,7 @@ using Reexport, Requires
 
 using ..LazySets: LazySet, ConvexSet, _witness_result_empty
 using Random: AbstractRNG, GLOBAL_RNG
+using ReachabilityBase.Commutative: @commutative
 using ReachabilityBase.Comparison: _rtol
 using ReachabilityBase.Distribution: reseed!
 using ReachabilityBase.Iteration: EmptyIterator
diff --git a/src/Sets/EmptySet/distance.jl b/src/Sets/EmptySet/distance.jl
index 4c5f38f100..48f8d3033b 100644
--- a/src/Sets/EmptySet/distance.jl
+++ b/src/Sets/EmptySet/distance.jl
@@ -1,3 +1,14 @@
+# distance point <-> set
+
+@commutative function distance(x::AbstractVector, ∅::EmptySet; p::Real=2)
+    @assert length(x) == dim(∅) "incompatible dimensions $(length(x)) and $(dim(∅))"
+
+    N = promote_type(eltype(x), eltype(∅))
+    return N(Inf)
+end
+
+# distance set <-> set
+
 function distance(∅₁::EmptySet, ∅₂::EmptySet; p::Real=2.0)
     return _distance_emptyset(∅₁, ∅₂; p=p)
 end
diff --git a/test/Sets/EmptySet.jl b/test/Sets/EmptySet.jl
index 6dc6e6889b..4ab91e5972 100644
--- a/test/Sets/EmptySet.jl
+++ b/test/Sets/EmptySet.jl
@@ -156,6 +156,13 @@ for N in [Float64, Rational{Int}, Float32]
     E2 = affine_map(ones(N, 3, 2), E, N[1, 1, 3])
     @test E2 isa EmptySet{N} && dim(E2) == 3
 
+    # distance (between point and set)
+    @test_throws AssertionError distance(E, N[0])
+    x = N[0, 0]
+    for res in (distance(E, x), distance(E, x))
+        @test res isa N && res == N(Inf)
+    end
+
     # exponential_map / linear_map
     for f in (exponential_map, linear_map)
         @test_throws AssertionError f(ones(N, 2, 3), E)
@@ -231,7 +238,7 @@ for N in [Float64, Rational{Int}, Float32]
     E2 = difference(B, E)
     @test E2 isa BallInf{N} && E2 == B
 
-    # distance
+    # distance (between sets)
     res = distance(E, E)
     @test res isa N && res == N(Inf)
     E2 = EmptySet{N}(3)