diff --git a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
index 5e03081750e..ae414761327 100644
--- a/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
+++ b/Homogeneous_kernel/include/CGAL/Homogeneous/function_objects.h
@@ -3098,7 +3098,16 @@ namespace HomogeneousKernelFunctors {
     }
 
     Point_2
-    operator()(const Line_2& l, const FT i) const
+    operator()(const Line_2& l, const RT& i) const
+    {
+      Point_2 p = K().construct_point_2_object()(l);
+      Vector_2 v = K().construct_vector_2_object()(l);
+      return K().construct_translated_point_2_object()
+                 (p, K().construct_scaled_vector_2_object()(v, i));
+    }
+
+    Point_2
+    operator()(const Line_2& l, const FT& i) const
     {
       Point_2 p = K().construct_point_2_object()(l);
       Vector_2 v = K().construct_vector_2_object()(l);
diff --git a/Kernel_23/include/CGAL/Line_2.h b/Kernel_23/include/CGAL/Line_2.h
index 89a46f34c26..d1bff5b4f8b 100644
--- a/Kernel_23/include/CGAL/Line_2.h
+++ b/Kernel_23/include/CGAL/Line_2.h
@@ -31,6 +31,7 @@
 #include <CGAL/Kernel/Return_base_tag.h>
 #include <CGAL/Dimension.h>
 #include <CGAL/IO/io.h>
+#include <CGAL/Kernel/mpl.h>
 
 namespace CGAL {
 
@@ -211,7 +212,19 @@ public:
   }
 
   Point_2
-  point(const FT i) const
+  point(const int i) const
+  {
+    return R().construct_point_2_object()(*this, RT(i));
+  }
+
+  Point_2
+  point(const RT& i) const
+  {
+    return R().construct_point_2_object()(*this,i);
+  }
+
+  Point_2
+  point(const typename First_if_different<FT, RT>::Type& i) const
   {
     return R().construct_point_2_object()(*this,i);
   }