diff --git a/geo-types/src/line.rs b/geo-types/src/line.rs
index f82ce430c..ed138dfcd 100644
--- a/geo-types/src/line.rs
+++ b/geo-types/src/line.rs
@@ -36,6 +36,53 @@ where
             end
         }
     }
+
+    /// Calculate the difference in ‘x’ components (Δx).
+    ///
+    /// Equivalent to:
+    ///
+    /// ```txt
+    /// line.end.x() - line.start.x()
+    /// ```
+    pub fn dx(&self) -> T {
+        self.end.x() - self.start.x()
+    }
+
+    /// Calculate the difference in ‘y’ components (Δy).
+    ///
+    /// Equivalent to:
+    ///
+    /// ```txt
+    /// line.end.y() - line.start.y()
+    /// ```
+    pub fn dy(&self) -> T {
+        self.end.y() - self.start.y()
+    }
+
+    /// Calculate the slope (Δy/Δx).
+    ///
+    /// Equivalent to:
+    ///
+    /// ```txt
+    /// line.dy() / line.dx()
+    /// ```
+    pub fn slope(&self) -> T {
+        self.dy() / self.dx()
+    }
+
+    /// Calculate the [determinant] of the line.
+    ///
+    /// Equivalent to:
+    ///
+    /// ```txt
+    /// line.start.x() * line.end.y() -
+    ///     line.start.y() * line.end.x()
+    /// ```
+    ///
+    /// [determinant]: https://en.wikipedia.org/wiki/Determinant
+    pub fn determinant(&self) -> T {
+        self.start.x() * self.end.y() - self.start.y() * self.end.x()
+    }
 }
 
 #[cfg(feature = "spade")]
diff --git a/geo/src/algorithm/centroid.rs b/geo/src/algorithm/centroid.rs
index f0e611d8c..1c93abc9b 100644
--- a/geo/src/algorithm/centroid.rs
+++ b/geo/src/algorithm/centroid.rs
@@ -37,7 +37,7 @@ where
     }
     let mut tmp = T::zero();
     for line in linestring.lines() {
-        tmp = tmp + (line.start.x() * line.end.y() - line.end.x() * line.start.y());
+        tmp = tmp + line.determinant();
     }
     tmp / (T::one() + T::one())
 }
@@ -55,7 +55,7 @@ where
     let mut sum_x = T::zero();
     let mut sum_y = T::zero();
     for line in poly_ext.lines() {
-        let tmp = line.start.x() * line.end.y() - line.end.x() * line.start.y();
+        let tmp = line.determinant();
         sum_x = sum_x + ((line.end.x() + line.start.x()) * tmp);
         sum_y = sum_y + ((line.end.y() + line.start.y()) * tmp);
     }
@@ -71,8 +71,8 @@ where
 
     fn centroid(&self) -> Self::Output {
         let two = T::one() + T::one();
-        let x = (self.start.x() + self.end.x()) / two;
-        let y = (self.start.y() + self.end.y()) / two;
+        let x = self.start.x() + self.dx() / two;
+        let y = self.start.y() + self.dy() / two;
         Point::new(x, y)
     }
 }
diff --git a/geo/src/algorithm/euclidean_distance.rs b/geo/src/algorithm/euclidean_distance.rs
index 309b025c6..c11aaa43c 100644
--- a/geo/src/algorithm/euclidean_distance.rs
+++ b/geo/src/algorithm/euclidean_distance.rs
@@ -4,6 +4,7 @@ use algorithm::polygon_distance_fast_path::*;
 use num_traits::float::FloatConst;
 use num_traits::{Float, Signed, ToPrimitive};
 use {Line, LineString, MultiLineString, MultiPoint, MultiPolygon, Point, Polygon};
+use algorithm::euclidean_length::EuclideanLength;
 
 use spade::rtree::RTree;
 use spade::SpadeFloat;
@@ -101,8 +102,7 @@ where
 {
     /// Minimum distance between two Points
     fn euclidean_distance(&self, p: &Point<T>) -> T {
-        let (dx, dy) = (self.x() - p.x(), self.y() - p.y());
-        dx.hypot(dy)
+        Line::new(*self, *p).euclidean_length()
     }
 }
 
diff --git a/geo/src/algorithm/euclidean_length.rs b/geo/src/algorithm/euclidean_length.rs
index 1c07b7547..16483282e 100644
--- a/geo/src/algorithm/euclidean_length.rs
+++ b/geo/src/algorithm/euclidean_length.rs
@@ -1,7 +1,6 @@
 use num_traits::Float;
 
 use ::{Line, LineString, MultiLineString};
-use algorithm::euclidean_distance::EuclideanDistance;
 
 /// Calculation of the length
 
@@ -30,7 +29,7 @@ where
     T: Float,
 {
     fn euclidean_length(&self) -> T {
-        self.start.euclidean_distance(&self.end)
+        self.dx().hypot(self.dy())
     }
 }
 
diff --git a/geo/src/algorithm/intersects.rs b/geo/src/algorithm/intersects.rs
index 56bd46bcc..42438e52b 100644
--- a/geo/src/algorithm/intersects.rs
+++ b/geo/src/algorithm/intersects.rs
@@ -29,17 +29,15 @@ where
     T: Float,
 {
     fn intersects(&self, p: &Point<T>) -> bool {
-        let dx = self.end.x() - self.start.x();
-        let dy = self.end.y() - self.start.y();
-        let tx = if dx == T::zero() {
+        let tx = if self.dx() == T::zero() {
             None
         } else {
-            Some((p.x() - self.start.x()) / dx)
+            Some((p.x() - self.start.x()) / self.dx())
         };
-        let ty = if dy == T::zero() {
+        let ty = if self.dy() == T::zero() {
             None
         } else {
-            Some((p.y() - self.start.y()) / dy)
+            Some((p.y() - self.start.y()) / self.dy())
         };
         match (tx, ty) {
             (None, None) => {
@@ -78,14 +76,12 @@ where
     fn intersects(&self, line: &Line<T>) -> bool {
         // Using Cramer's Rule:
         // https://en.wikipedia.org/wiki/Intersection_%28Euclidean_geometry%29#Two_line_segments
-        let (x1, y1, x2, y2) = (self.start.x(), self.start.y(), self.end.x(), self.end.y());
-        let (x3, y3, x4, y4) = (line.start.x(), line.start.y(), line.end.x(), line.end.y());
-        let a1 = x2 - x1;
-        let a2 = y2 - y1;
-        let b1 = x3 - x4; // == -(x4 - x3)
-        let b2 = y3 - y4; // == -(y4 - y3)
-        let c1 = x3 - x1;
-        let c2 = y3 - y1;
+        let a1 = self.dx();
+        let a2 = self.dy();
+        let b1 = -line.dx();
+        let b2 = -line.dy();
+        let c1 = line.start.x() - self.start.x();
+        let c2 = line.start.y() - self.start.y();
 
         let d = a1 * b2 - a2 * b1;
         if d == T::zero() {
@@ -149,15 +145,14 @@ where
         }
         for a in self.lines() {
             for b in linestring.lines() {
-                let u_b = (b.end.y() - b.start.y()) * (a.end.x() - a.start.x())
-                    - (b.end.x() - b.start.x()) * (a.end.y() - a.start.y());
+                let u_b = b.dy() * a.dx() - b.dx() * a.dy();
                 if u_b == T::zero() {
                     continue;
                 }
-                let ua_t = (b.end.x() - b.start.x()) * (a.start.y() - b.start.y())
-                    - (b.end.y() - b.start.y()) * (a.start.x() - b.start.x());
-                let ub_t = (a.end.x() - a.start.x()) * (a.start.y() - b.start.y())
-                    - (a.end.y() - a.start.y()) * (a.start.x() - b.start.x());
+                let ua_t = b.dx() * (a.start.y() - b.start.y())
+                    - b.dy() * (a.start.x() - b.start.x());
+                let ub_t = a.dx() * (a.start.y() - b.start.y())
+                    - a.dy() * (a.start.x() - b.start.x());
                 let u_a = ua_t / u_b;
                 let u_b = ub_t / u_b;
                 if (T::zero() <= u_a) && (u_a <= T::one()) && (T::zero() <= u_b)
diff --git a/geo/src/algorithm/polygon_distance_fast_path.rs b/geo/src/algorithm/polygon_distance_fast_path.rs
index 04dfbbb5f..7ea1c22f6 100644
--- a/geo/src/algorithm/polygon_distance_fast_path.rs
+++ b/geo/src/algorithm/polygon_distance_fast_path.rs
@@ -139,7 +139,7 @@ where
             if pprev.x() > p.x() {
                 if pprev.y() >= p.y() && pnext.y() >= p.y() {
                     if *slope > T::zero() {
-                        slope_prev = (pprev.y() - p.y()) / (pprev.x() - p.x());
+                        slope_prev = Line::new(*p, pprev).slope();
                         if clockwise && *slope <= slope_prev || !clockwise && *slope >= slope_prev {
                             cos = -cos;
                             sin = -sin;
@@ -156,8 +156,8 @@ where
                             sin = -sin;
                         }
                     } else {
-                        slope_prev = (pprev.y() - p.y()) / (pprev.x() - p.x());
-                        slope_next = (pnext.y() - p.y()) / (pnext.x() - p.x());
+                        slope_prev = Line::new(*p, pprev).slope();
+                        slope_next = Line::new(*p, pnext).slope();
                         if clockwise {
                             if *slope <= slope_prev {
                                 cos = -cos;
@@ -192,8 +192,8 @@ where
                             sin = -sin;
                         }
                     } else {
-                        slope_prev = (p.y() - pprev.y()) / (p.x() - pprev.x());
-                        slope_next = (p.y() - pnext.y()) / (p.x() - pnext.x());
+                        slope_prev = Line::new(*p, pprev).slope();
+                        slope_next = Line::new(*p, pnext).slope();
                         if clockwise {
                             if *slope <= slope_prev {
                                 sin = -sin;
@@ -208,7 +208,7 @@ where
                     }
                 } else if pprev.y() <= p.y() && pnext.y() <= p.y() {
                     if *slope > T::zero() {
-                        slope_next = (p.y() - pnext.y()) / (p.x() - pnext.x());
+                        slope_next = Line::new(*p, pnext).slope();
                         if *slope >= slope_next {
                             cos = -cos;
                             sin = -sin;
@@ -274,9 +274,9 @@ where
     let slope = if vertical || p.y() == u.y() {
         T::zero()
     } else if u.x() > p.x() {
-        (u.y() - p.y()) / (u.x() - p.x())
+        Line::new(*p, *u).slope()
     } else {
-        (p.y() - u.y()) / (p.x() - u.x())
+        Line::new(*u, *p).slope()
     };
     let upx;
     let upy;
@@ -402,9 +402,9 @@ fn triangle_area<T>(a: &Point<T>, b: &Point<T>, c: &Point<T>) -> T
 where
     T: Float,
 {
-    (T::from(0.5).unwrap()
-        * (a.x() * b.y() - a.y() * b.x() + a.y() * c.x() - a.x() * c.y() + b.x() * c.y()
-            - c.x() * b.y()))
+      (Line::new(*a, *b).determinant() +
+         Line::new(*b, *c).determinant() +
+         Line::new(*c, *a).determinant()) / (T::one() + T::one())
 }
 
 /// Does abc turn left?
@@ -491,13 +491,11 @@ where
             }
             false => {
                 state.vertical = false;
-                if state.p1.x() > state.p1next.x() {
-                    state.slope =
-                        (state.p1.y() - state.p1next.y()) / (state.p1.x() - state.p1next.x());
+                state.slope = if state.p1.x() > state.p1next.x() {
+                    Line::new(state.p1next, state.p1).slope()
                 } else {
-                    state.slope =
-                        (state.p1next.y() - state.p1.y()) / (state.p1next.x() - state.p1.x());
-                }
+                    Line::new(state.p1, state.p1next).slope()
+                };
             }
         }
     }
@@ -510,13 +508,11 @@ where
             }
             false => {
                 state.vertical = false;
-                if state.q2.x() > state.q2next.x() {
-                    state.slope =
-                        (state.q2.y() - state.q2next.y()) / (state.q2.x() - state.q2next.x());
+                state.slope = if state.q2.x() > state.q2next.x() {
+                    Line::new(state.q2next, state.q2).slope()
                 } else {
-                    state.slope =
-                        (state.q2next.y() - state.q2.y()) / (state.q2next.x() - state.q2.x());
-                }
+                    Line::new(state.q2, state.q2next).slope()
+                };
             }
         }
     }
diff --git a/geo/src/algorithm/simplify.rs b/geo/src/algorithm/simplify.rs
index 5f86502ef..bee42924e 100644
--- a/geo/src/algorithm/simplify.rs
+++ b/geo/src/algorithm/simplify.rs
@@ -1,5 +1,5 @@
 use num_traits::Float;
-use ::{LineString, MultiLineString, MultiPolygon, Point, Polygon};
+use ::{LineString, MultiLineString, MultiPolygon, Point, Polygon, Line};
 use algorithm::euclidean_distance::EuclideanDistance;
 
 // perpendicular distance from a point to a line
diff --git a/geo/src/algorithm/winding_order.rs b/geo/src/algorithm/winding_order.rs
index dff0affcd..a86936935 100644
--- a/geo/src/algorithm/winding_order.rs
+++ b/geo/src/algorithm/winding_order.rs
@@ -8,7 +8,7 @@ pub(crate) fn twice_signed_ring_area<T>(linestring: &LineString<T>) -> T where T
     }
     let mut tmp = T::zero();
     for line in linestring.lines() {
-        tmp = tmp + (line.start.x() * line.end.y() - line.end.x() * line.start.y());
+        tmp = tmp + line.determinant();
     }
 
     tmp