diff --git a/NEWS.md b/NEWS.md
index b605e1a622..1f555c9cb7 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -4,6 +4,7 @@
 - Fixes/Improvements:
   - Fix ConcaveHullOfPolygons nested shell handling (GH-1169, Martin Davis)
   - Fix RelateNG for computing IM for empty-nonempty cases (Martin Davis)
+  - Fix LineString->getPoint(n) for M geometries (GH-1191, @hsieyuan)
 
 ## Changes in 3.13.0
 2024-09-06
diff --git a/src/geom/SimpleCurve.cpp b/src/geom/SimpleCurve.cpp
index be9b50b443..dcbaf7114b 100644
--- a/src/geom/SimpleCurve.cpp
+++ b/src/geom/SimpleCurve.cpp
@@ -251,7 +251,16 @@ SimpleCurve::getPointN(std::size_t n) const
 {
     assert(getFactory());
     assert(points.get());
-    return std::unique_ptr<Point>(getFactory()->createPoint(points->getAt(n)));
+    if (hasM() || hasZ()) {
+        CoordinateXYZM c;
+        points->getAt(n, c);
+        return getFactory()->createPoint(c);
+    }
+    else {
+        CoordinateXY c;
+        points->getAt(n, c);
+        return getFactory()->createPoint(c);
+    }
 }
 
 std::unique_ptr<Point>
diff --git a/tests/unit/geom/LineStringTest.cpp b/tests/unit/geom/LineStringTest.cpp
index 26a8756bfb..1e1136fce5 100644
--- a/tests/unit/geom/LineStringTest.cpp
+++ b/tests/unit/geom/LineStringTest.cpp
@@ -13,6 +13,7 @@
 #include <geos/geom/GeometryFactory.h>
 #include <geos/geom/PrecisionModel.h>
 #include <geos/io/WKTReader.h>
+#include <geos/io/WKTWriter.h>
 #include <geos/util/GEOSException.h>
 #include <geos/util/IllegalArgumentException.h>
 #include <geos/constants.h>
@@ -35,6 +36,7 @@ struct test_linestring_data {
     geos::geom::PrecisionModel pm_;
     geos::geom::GeometryFactory::Ptr factory_;
     geos::io::WKTReader reader_;
+    geos::io::WKTWriter writer_;
 
     std::unique_ptr<geos::geom::LineString> empty_line_;
     std::unique_ptr<geos::geom::LineString> line_;
@@ -588,5 +590,23 @@ void object::test<32>
     ensure(!line_->hasDimension(geos::geom::Dimension::A));
 }
 
+
+// https://github.com/libgeos/geos/issues/1191
+// line->getPoint(n) loses M dimension
+template<>
+template<>
+void object::test<33>
+()
+{
+    auto geom = reader_.read("LINESTRING M (0 1 2, 10 11 12, 20 21 22)");
+    ensure(geom != nullptr);
+    geos::geom::LineString *line = static_cast<LineString*>(geom.get());
+    ensure_equals(line->getCoordinateDimension(), 3);
+    auto pt = line->getPointN(2);
+    auto out = writer_.write(*pt);
+    ensure_equals(out, "POINT M (20 21 22)");
+}
+
+
 } // namespace tut