diff --git a/common/src/app/common/geom/shapes/transforms.cljc b/common/src/app/common/geom/shapes/transforms.cljc
index 7ba56f2197..d0cd0614aa 100644
--- a/common/src/app/common/geom/shapes/transforms.cljc
+++ b/common/src/app/common/geom/shapes/transforms.cljc
@@ -297,19 +297,26 @@
 
         yv1     (gpt/to-vec p0' (nth points' 3))
         yv2     (gpt/to-vec p0  (nth points 3))
-        dot-y   (gpt/dot yv1 yv2)]
+        dot-y   (gpt/dot yv1 yv2)
+
+        ;; A right-angle turn has a zero dot product. Coordinate roundoff
+        ;; must not turn that into a reflection, regardless of shape size.
+        flip-x? (and (neg? dot-x)
+                     (not (mth/close? dot-x 0 (* 1e-10 (gpt/length xv1) (gpt/length xv2)))))
+        flip-y? (and (neg? dot-y)
+                     (not (mth/close? dot-y 0 (* 1e-10 (gpt/length yv1) (gpt/length yv2)))))]
 
     (cond-> shape
-      (neg? dot-x)
+      flip-x?
       (update :flip-x not)
 
-      (neg? dot-y)
+      flip-y?
       (update :flip-y not)
 
       ;; Negate rotation only when an odd number of axes are flipped,
       ;; since flipping both axes is equivalent to a 180° rotation and
       ;; two negations would cancel each other out.
-      (not= (neg? dot-x) (neg? dot-y))
+      (not= flip-x? flip-y?)
       (update :rotation -))))
 
 (defn- apply-transform-move
diff --git a/common/test/common_tests/geom_shapes_test.cljc b/common/test/common_tests/geom_shapes_test.cljc
index e60ded0fe7..7a3023522b 100644
--- a/common/test/common_tests/geom_shapes_test.cljc
+++ b/common/test/common_tests/geom_shapes_test.cljc
@@ -271,3 +271,14 @@
       (t/is (true? (:flip-y result)))
       ;; rotation must not be negated when both axes are flipped
       (t/is (mth/close? 30 (:rotation result))))))
+
+(t/deftest a-right-angle-turn-does-not-invent-a-flip-from-roundoff
+  (doseq [size [0.01 100 1000000]]
+    (let [shape (create-test-shape :rect {:width size :height size :rotation 90})
+          shape (assoc shape :points [(gpt/point size 0) (gpt/point size size)
+                                      (gpt/point 0 size) (gpt/point 0 (* size 1e-14))])
+          turn (gmt/transform-in (gpt/point (/ size 2) (/ size 2)) (gmt/rotate-matrix 90))
+          after (gsh/apply-transform (assoc-in shape [:modifiers :rotation] 90) turn)]
+      (t/is (not (:flip-x after)))
+      (t/is (not (:flip-y after)))
+      (t/is (mth/close? 180 (:rotation after))))))