diff --git a/README.md b/README.md
index c3f0ee44f..adc3f550b 100644
--- a/README.md
+++ b/README.md
@@ -295,6 +295,7 @@ If you code with [TypeScript](http://www.typescriptlang.org/) there are comprehe
 
 ### Updates
 
+* Added an `epsilon` argument for fuzzy comparisons in Phaser.Line#pointOnLine and Phaser.Line#pointOnSegment (#312).
 * Removed obsolete PIXI TypeScript definitions.
 * Removed [filters/pixi](https://github.com/photonstorm/phaser-ce/tree/v2.8.3/filters/pixi). They require PIXI.AbstractFilter, which was removed in 2.7.0.
 * Updated NPM dependencies (except [typescript](https://www.npmjs.com/package/typescript); photonstorm/phaser#2198) and added [package-lock.json](https://docs.npmjs.com/files/package-lock.json).
diff --git a/src/geom/Line.js b/src/geom/Line.js
index d53bfd502..ce4e55149 100644
--- a/src/geom/Line.js
+++ b/src/geom/Line.js
@@ -222,35 +222,37 @@ Phaser.Line.prototype = {
     },
 
     /**
-    * Tests if the given coordinates fall on this line. See pointOnSegment to test against just the line segment.
+    * Tests if the given coordinates fall on this line. See {@link #pointOnSegment} to test against just the line segment.
     *
     * @method Phaser.Line#pointOnLine
     * @param {number} x - The line to check against this one.
     * @param {number} y - The line to check against this one.
+    * @param {number} [epsilon=0] - Range for a fuzzy comparison, e.g., 0.0001.
     * @return {boolean} True if the point is on the line, false if not.
     */
-    pointOnLine: function (x, y) {
+    pointOnLine: function (x, y, epsilon) {
 
-        return ((x - this.start.x) * (this.end.y - this.start.y) === (this.end.x - this.start.x) * (y - this.start.y));
+        return Phaser.Math.fuzzyEqual((x - this.start.x) * (this.end.y - this.start.y), (this.end.x - this.start.x) * (y - this.start.y), epsilon || 0);
 
     },
 
     /**
-    * Tests if the given coordinates fall on this line and within the segment. See pointOnLine to test against just the line.
+    * Tests if the given coordinates fall on this line and within the segment. See {@link #pointOnLine} to test against just the line.
     *
     * @method Phaser.Line#pointOnSegment
     * @param {number} x - The line to check against this one.
     * @param {number} y - The line to check against this one.
+    * @param {number} [epsilon=0] - Range for a fuzzy comparison, e.g., 0.0001.
     * @return {boolean} True if the point is on the line and segment, false if not.
     */
-    pointOnSegment: function (x, y) {
+    pointOnSegment: function (x, y, epsilon) {
 
         var xMin = Math.min(this.start.x, this.end.x);
         var xMax = Math.max(this.start.x, this.end.x);
         var yMin = Math.min(this.start.y, this.end.y);
         var yMax = Math.max(this.start.y, this.end.y);
 
-        return (this.pointOnLine(x, y) && (x >= xMin && x <= xMax) && (y >= yMin && y <= yMax));
+        return (this.pointOnLine(x, y, epsilon) && (x >= xMin && x <= xMax) && (y >= yMin && y <= yMax));
 
     },
 
diff --git a/typescript/phaser.d.ts b/typescript/phaser.d.ts
index 3a204675c..8da28ecbd 100644
--- a/typescript/phaser.d.ts
+++ b/typescript/phaser.d.ts
@@ -2467,8 +2467,8 @@ declare module Phaser {
         fromSprite(startSprite: Phaser.Sprite, endSprite: Phaser.Sprite, useCenter?: boolean): Phaser.Line;
         intersects(line: Phaser.Line, asSegment?: boolean, result?: Phaser.Point): Phaser.Point;
         midPoint(out?: Phaser.Point): Phaser.Point;
-        pointOnLine(x: number, y: number): boolean;
-        pointOnSegment(x: number, y: number): boolean;
+        pointOnLine(x: number, y: number, epsilon?: number): boolean;
+        pointOnSegment(x: number, y: number, epsilon?: number): boolean;
         random(out?: Phaser.Point): Phaser.Point;
         reflect(line: Phaser.Line): number;
         rotate(angle: number, asDegrees?: boolean): Phaser.Line;