diff --git a/crates/engine/src/cmd/sketch.rs b/crates/engine/src/cmd/sketch.rs
index 33ede42e..181d69d3 100644
--- a/crates/engine/src/cmd/sketch.rs
+++ b/crates/engine/src/cmd/sketch.rs
@@ -167,7 +167,7 @@ pub static COMMANDS: &[CommandSpec] = &[
         .at("SKETCH", "CONSTRAINTS")
         .icon("c_symmetry")
         .enabled(in_sketch)
-        .params("a, b: two points or two curves (lines mirror their ends, circles/arcs their centres); line: symmetry line id, or x / y for the sketch's own axes (a curve with that id wins; an axis becomes a linked construction line on it, reported in created)"),
+        .params("a, b: two points or two curves (lines mirror their ends, circles/arcs their centres); line: symmetry line id, or x / y for the sketch's own axes (a curve with that id wins; an axis becomes a linked construction line on it, reported in created); or point (or a point id as line, \"origin\" too): symmetric about that point, each pair joined by a construction line it is the midpoint of"),
     CommandSpec::new("sketch.construction", "Normal/Construction", construction)
         .at("SKETCH", "CREATE")
         .icon("construction")
@@ -1676,9 +1676,38 @@ fn c_midpoint(s: &mut Session, p: &Value) -> Result<Value> {
         Ok(ConstraintKind::Midpoint { p: point_ref(sk, p.get("point"), cmd, "point")?, l: curve_ref(sk, p.get("line"), cmd, "line")? })
     })
 }
+/// The centre of a symmetry about a point (#1075): `point`, or `line` naming a point rather than
+/// a curve or a sketch axis (the origin picked as the third entity).
+fn symmetry_center(sk: &Sketch, p: &Value, cmd: &str) -> Result<Option<usize>> {
+    if let Some(r) = p.get("point") {
+        return point_ref(sk, Some(r), cmd, "point").map(Some);
+    }
+    let Some(id) = p.get("line").and_then(Value::as_str) else { return Ok(None) };
+    if sk.curve_index(id).is_some() || matches!(id, "x" | "y") {
+        return Ok(None);
+    }
+    Ok(sk.resolve_point(id))
+}
+
+/// Points `a` and `b` symmetric about point `c`: a construction line from `a` to `b` with `c`
+/// at its midpoint.
+fn symmetric_about_point(sk: &mut Sketch, a: usize, b: usize, c: usize, cmd: &str) -> Result<String> {
+    if a == b || a == c || b == c {
+        return Err(bad(cmd, "symmetry about a point needs two other points"));
+    }
+    let l = sk.add_line_pts(a, b, None)?;
+    if let Some(cu) = sk.curves.get_mut(l) {
+        cu.construction = true;
+    }
+    add_c(sk, ConstraintKind::Midpoint { p: c, l })
+}
+
 fn c_symmetry(s: &mut Session, p: &Value) -> Result<Value> {
     let cmd = "sketch.constraint.symmetry";
     let (ids, info) = edit(s, p, cmd, true, |sk, _| {
+        if let Some(c) = symmetry_center(sk, p, cmd)? {
+            return symmetry_about_point(sk, p, c, cmd);
+        }
         let l = line_or_axis_ref(sk, p.get("line"), cmd, "line")?;
         let ra = p.get("a").and_then(Value::as_str).ok_or_else(|| bad(cmd, "`a` must be a point or curve"))?;
         let rb = p.get("b").and_then(Value::as_str).ok_or_else(|| bad(cmd, "`b` must be a point or curve"))?;
@@ -1716,6 +1745,52 @@ fn c_symmetry(s: &mut Session, p: &Value) -> Result<Value> {
     Ok(json!({"constraints": ids, "sketch": info}))
 }
 
+/// Symmetry about point `c`: two points, two circles/arcs (their centres, and equal radii) or two
+/// lines (each end with the end of the other line nearest its mirror image). The constraints
+/// (the construction lines show in the response's `created`).
+fn symmetry_about_point(sk: &mut Sketch, p: &Value, c: usize, cmd: &str) -> Result<Vec<String>> {
+    let ra = p.get("a").and_then(Value::as_str).ok_or_else(|| bad(cmd, "`a` must be a point or curve"))?;
+    let rb = p.get("b").and_then(Value::as_str).ok_or_else(|| bad(cmd, "`b` must be a point or curve"))?;
+    let rep = solve(&mut sk.clone());
+    let order = ent(sk, ra).zip(ent(sk, rb));
+    let pairs: Vec<(usize, usize)> = match (sk.resolve_point(ra), sk.resolve_point(rb)) {
+        (Some(a), Some(b)) => vec![(a, b)],
+        _ => {
+            let ca = sk.curve_index(ra).ok_or_else(|| bad(cmd, format!("unknown entity `{ra}`")))?;
+            let cb = sk.curve_index(rb).ok_or_else(|| bad(cmd, format!("unknown entity `{rb}`")))?;
+            match (sk.curves.get(ca).map(|x| x.kind.clone()), sk.curves.get(cb).map(|x| x.kind.clone())) {
+                (Some(CurveKind::Line { a: a0, b: a1 }), Some(CurveKind::Line { a: b0, b: b1 })) => {
+                    let pc = sk.point(c).unwrap_or_default();
+                    let mirror = |i: usize| pc * 2.0 - sk.point(i).unwrap_or_default();
+                    let near = |i: usize, j: usize| mirror(i).dist(sk.point(j).unwrap_or_default());
+                    if near(a0, b0) + near(a1, b1) <= near(a0, b1) + near(a1, b0) { vec![(a0, b0), (a1, b1)] } else { vec![(a0, b1), (a1, b0)] }
+                }
+                (Some(_), Some(_)) => {
+                    let pa = round_center(sk, ca).ok_or_else(|| bad(cmd, "symmetry needs two lines or two circles/arcs"))?;
+                    let pb = round_center(sk, cb).ok_or_else(|| bad(cmd, "symmetry needs two lines or two circles/arcs"))?;
+                    let mut out = symmetry_pairs(sk, &[(pa, pb)], c, cmd)?;
+                    out.push(add_c(sk, ConstraintKind::Equal { a: ca, b: cb })?);
+                    if let Some((a, b)) = order {
+                        apply_in_order(sk, &rep, &[a, Ent::Point(c)], b, cmd)?;
+                    }
+                    return Ok(out);
+                }
+                _ => return Err(bad(cmd, "symmetry needs two points or two curves")),
+            }
+        }
+    };
+    let out = symmetry_pairs(sk, &pairs, c, cmd)?;
+    // The first entity and the centre stay; the second mirrors onto it.
+    if let Some((a, b)) = order {
+        apply_in_order(sk, &rep, &[a, Ent::Point(c)], b, cmd)?;
+    }
+    Ok(out)
+}
+
+fn symmetry_pairs(sk: &mut Sketch, pairs: &[(usize, usize)], c: usize, cmd: &str) -> Result<Vec<String>> {
+    pairs.iter().map(|(a, b)| symmetric_about_point(sk, *a, *b, c, cmd)).collect()
+}
+
 fn round_center(sk: &Sketch, c: usize) -> Option<usize> {
     match sk.curves.get(c)?.kind {
         CurveKind::Circle { c, .. } | CurveKind::Arc { c, .. } => Some(c),
@@ -2411,3 +2486,6 @@ mod ids_tests;
 #[cfg(test)]
 #[path = "sketch_redundant_tests.rs"]
 mod redundant_tests;
+#[cfg(test)]
+#[path = "sketch_symmetry_point_tests.rs"]
+mod symmetry_point_tests;
diff --git a/crates/engine/src/cmd/sketch_symmetry_point_tests.rs b/crates/engine/src/cmd/sketch_symmetry_point_tests.rs
new file mode 100644
index 00000000..05077e11
--- /dev/null
+++ b/crates/engine/src/cmd/sketch_symmetry_point_tests.rs
@@ -0,0 +1,87 @@
+//! Symmetry about a point (#1075): the origin (or any sketch point) picked as the third entity,
+//! or given as `point`. Each pair is joined by a construction line the point is the midpoint of.
+
+use serde_json::{Value, json};
+use solidcraft_geom::Vec2;
+use solidcraft_sketch::{ConstraintKind, Sketch};
+
+use crate::Session;
+
+fn run(s: &mut Session, id: &str, p: Value) -> Value {
+    match s.execute(id, &p) {
+        Ok(v) => v,
+        Err(e) => panic!("{id} {p}: {e}"),
+    }
+}
+
+fn sketch(s: &Session) -> Sketch {
+    s.doc.sketch(s.active_sketch.unwrap()).unwrap().clone()
+}
+
+fn pt(sk: &Sketch, r: &str) -> Vec2 {
+    sk.point(sk.resolve_point(r).unwrap()).unwrap()
+}
+
+fn new_sketch() -> Session {
+    let mut s = Session::default();
+    run(&mut s, "sketch.create", json!({"plane": "XY"}));
+    s
+}
+
+#[test]
+fn two_points_symmetric_about_the_origin() {
+    for params in [json!({"a": "p", "b": "q", "line": "origin"}), json!({"a": "p", "b": "q", "point": "origin"})] {
+        let mut s = new_sketch();
+        run(&mut s, "sketch.point", json!({"point": [10, 5], "id": "p"}));
+        run(&mut s, "sketch.point", json!({"point": [-12, -3], "id": "q"}));
+        let r = run(&mut s, "sketch.constraint.symmetry", params.clone());
+        let sk = sketch(&s);
+        // The first point stays; the second mirrors onto it through the origin.
+        assert!(pt(&sk, "p").dist(Vec2::new(10.0, 5.0)) < 1e-6, "{params}");
+        assert!(pt(&sk, "q").dist(Vec2::new(-10.0, -5.0)) < 1e-6, "{params}: {:?}", pt(&sk, "q"));
+        // One construction line, from p to q, with the origin at its midpoint.
+        let created = r["created"]["curves"].as_array().unwrap();
+        assert_eq!(created.len(), 1, "{r}");
+        let l = sk.curve_index(created[0].as_str().unwrap()).unwrap();
+        assert!(sk.curves[l].construction);
+        assert!(sk.constraints.iter().any(|k| k.kind == ConstraintKind::Midpoint { p: 0, l }));
+        // It holds: moving p moves q opposite.
+        run(&mut s, "sketch.drag", json!({"entity": "p", "from": [10, 5], "to": [20, 8]}));
+        let sk = sketch(&s);
+        assert!((pt(&sk, "p") + pt(&sk, "q")).len() < 1e-6, "{:?} {:?}", pt(&sk, "p"), pt(&sk, "q"));
+    }
+}
+
+#[test]
+fn circles_and_lines_symmetric_about_a_point() {
+    let mut s = new_sketch();
+    run(&mut s, "sketch.point", json!({"point": [5, 5], "id": "c"}));
+    run(&mut s, "sketch.circle.center", json!({"center": [15, 5], "radius": 2, "id": "k1"}));
+    run(&mut s, "sketch.circle.center", json!({"center": [-4, 6], "radius": 3, "id": "k2"}));
+    run(&mut s, "sketch.constraint.symmetry", json!({"a": "k1", "b": "k2", "point": "c"}));
+    let sk = sketch(&s);
+    let (c1, c2) = (sk.center(sk.curve_index("k1").unwrap()).unwrap(), sk.center(sk.curve_index("k2").unwrap()).unwrap());
+    assert!(((c1 + c2) * 0.5).dist(Vec2::new(5.0, 5.0)) < 1e-6, "{c1:?} {c2:?}");
+    assert!((sk.radius(sk.curve_index("k1").unwrap()).unwrap() - sk.radius(sk.curve_index("k2").unwrap()).unwrap()).abs() < 1e-6);
+
+    // Two lines: each end pairs with the other line's end nearest its mirror image.
+    let mut s = new_sketch();
+    run(&mut s, "sketch.line", json!({"points": [[2, 1], [8, 4]], "ids": ["a"]}));
+    run(&mut s, "sketch.line", json!({"points": [[-7, -5], [-1, -1]], "ids": ["b"]}));
+    let r = run(&mut s, "sketch.constraint.symmetry", json!({"a": "a", "b": "b", "line": "origin"}));
+    assert_eq!(r["created"]["curves"].as_array().unwrap().len(), 2, "{r}");
+    let sk = sketch(&s);
+    assert!((pt(&sk, "a.start") + pt(&sk, "b.end")).len() < 1e-6);
+    assert!((pt(&sk, "a.end") + pt(&sk, "b.start")).len() < 1e-6);
+}
+
+#[test]
+fn a_point_cannot_be_its_own_mirror() {
+    let mut s = new_sketch();
+    run(&mut s, "sketch.point", json!({"point": [10, 5], "id": "p"}));
+    let before = s.doc.to_json();
+    assert!(s.execute("sketch.constraint.symmetry", &json!({"a": "p", "b": "origin", "point": "origin"})).is_err());
+    assert!(s.execute("sketch.constraint.symmetry", &json!({"a": "p", "b": "p", "line": "origin"})).is_err());
+    assert!(s.execute("sketch.constraint.symmetry", &json!({"a": "p", "b": "origin", "point": "nope"})).is_err());
+    assert_eq!(s.doc.to_json(), before);
+}
diff --git a/crates/ui-egui/src/symmetry_pick_tests.rs b/crates/ui-egui/src/symmetry_pick_tests.rs
new file mode 100644
index 00000000..d2ecae50
--- /dev/null
+++ b/crates/ui-egui/src/symmetry_pick_tests.rs
@@ -0,0 +1,46 @@
+//! The Symmetry tool's third pick may be the origin point or an origin axis (#1075).
+
+use serde_json::json;
+use solidcraft_engine::geom::Vec2;
+
+use crate::scenario::Harness;
+
+/// An XY sketch with points p (10, 5) and q (-12, -3), the Symmetry tool started and both picked.
+fn two_points_picked() -> Harness {
+    let mut h = Harness::new();
+    h.app.ui.show_origin = true;
+    h.app.run("sketch.create", json!({"plane":"XY"})).unwrap();
+    h.app.run("sketch.point", json!({"point":[10,5],"id":"p"})).unwrap();
+    h.app.run("sketch.point", json!({"point":[-12,-3],"id":"q"})).unwrap();
+    h.app.cam.distance = 120.0;
+    h.settle();
+    h.app.start("sketch.constraint.symmetry");
+    for xy in [[10, 5], [-12, -3]] {
+        let at = h.call("ui.at", json!({ "sketch": xy }))["result"].clone();
+        h.step(&json!({ "click": at })).unwrap();
+    }
+    h
+}
+
+fn point(h: &Harness, id: &str) -> Vec2 {
+    let sk = h.app.session.doc.sketch(h.app.session.active_sketch.unwrap()).unwrap();
+    sk.point(sk.resolve_point(id).unwrap()).unwrap()
+}
+
+#[test]
+fn symmetry_about_the_origin_point() {
+    let mut h = two_points_picked();
+    let at = h.call("ui.at", json!({"sketch":[0,0]}))["result"].clone();
+    h.step(&json!({ "click": at })).unwrap();
+    assert!((point(&h, "p") + point(&h, "q")).len() < 1e-6, "{:?} {:?}", point(&h, "p"), point(&h, "q"));
+}
+
+#[test]
+fn symmetry_about_an_origin_axis() {
+    let mut h = two_points_picked();
+    // On the Y axis, away from the origin point and from p and q.
+    let at = h.call("ui.at", json!({"sketch":[0,6]}))["result"].clone();
+    h.step(&json!({ "click": at })).unwrap();
+    let (p, q) = (point(&h, "p"), point(&h, "q"));
+    assert!((p.x + q.x).abs() < 1e-6 && (p.y - q.y).abs() < 1e-6, "mirrored in the Y axis: {p:?} {q:?}");
+}
diff --git a/crates/ui-egui/src/tools.rs b/crates/ui-egui/src/tools.rs
index eb62739a..1f643373 100644
--- a/crates/ui-egui/src/tools.rs
+++ b/crates/ui-egui/src/tools.rs
@@ -16,6 +16,10 @@ mod display_preview_tests;
 #[path = "sketch_neutral_click_tests.rs"]
 mod neutral_click_tests;
 
+#[cfg(test)]
+#[path = "symmetry_pick_tests.rs"]
+mod symmetry_pick_tests;
+
 #[derive(Clone, Copy, Debug, PartialEq, Eq)]
 pub enum Kind {
     /// Click points; `n` points complete the shape (0 = chain until finished).
@@ -189,8 +193,12 @@ pub fn on_click(app: &mut SolveApp, proj: &Proj, pos: Pos2) {
         }
         Kind::Pick(n) => {
             let hits = pick(app, proj, pos);
+            // Symmetry's third pick may be an origin axis lying along the sketch's own x or y
+            // (#1075); the command names those `x` / `y`.
+            let axis_ok = tool.cmd == "sketch.constraint.symmetry" && tool.picks.len() == 2;
             if let Some(id) = hits.iter().find_map(|h| match h {
                 Hit::SketchPoint { id, .. } | Hit::SketchCurve { id, .. } => Some(id.clone()),
+                Hit::Axis { name } if axis_ok => sketch_axis_of(app, name).map(str::to_string),
                 _ => None,
             }) {
                 tool.picks.push(id);
@@ -455,6 +463,31 @@ pub(crate) fn projection_preselection(selection: &[solidcraft_engine::Sel]) -> O
         .collect()
 }
 
+/// `x` or `y` when the origin axis `name` is the active sketch's own x or y axis: along it, and
+/// through the sketch's origin.
+fn sketch_axis_of(app: &SolveApp, name: &str) -> Option<&'static str> {
+    use solidcraft_engine::geom::Vec3;
+    let dir = match name {
+        "X" => Vec3::X,
+        "Y" => Vec3::Y,
+        "Z" => Vec3::Z,
+        _ => return None,
+    };
+    let st = app.session.world_state();
+    let plane = st.sketch(app.session.active_sketch?)?.plane;
+    let o = plane.origin;
+    if (o - dir * o.dot(dir)).len() > 1e-6 {
+        return None;
+    }
+    if plane.x.dot(dir).abs() > 1.0 - 1e-9 {
+        Some("x")
+    } else if plane.y.dot(dir).abs() > 1.0 - 1e-9 {
+        Some("y")
+    } else {
+        None
+    }
+}
+
 fn run_pick(app: &mut SolveApp, t: &Tool) {
     let k = &t.picks;
     let params = match t.cmd {