TypeScript - calculate distance between two points with Pythagorean equation

In this article, we would like to show you how to calculate the distance between two points with the Pythagorean equation using TypeScript.

Quick solution:

// P1 = (x1, y1); P2 = (x2, y2)
const a = x2 - x1;
const b = y2 - y1;
const distance = Math.sqrt(a * a + b * b);

Quick example:

// ONLINE-RUNNER:browser;

const a = 3 - 1;
const b = 3 - 1;
const distance = Math.sqrt(a * a + b * b);

console.log(distance); // 2.8284271247461903

1. Mathematical theorem on the coordinate system

Distance calculation for points requires starting with the transformation of the Pythagorean equation to the point version.

a^2 + b^2 = c^2 => c = sqrt(a^2 + b^2)

a = |x2 - x1|

b = |y2 - y1|

c = sqrt(|x2 - x1|^2 + |y2 - y1|^2)

what can be transformed to:

c = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance between P1 and P2 is equal to c

Note: absolute value of a and b can be avoided because of squares inside Pythagorean equation - squares remove minuses.

Example calculations:

a = |x2 - x1| = |3 - 7| = 4

b = |y2 - y1| = |5 - 2| = 3

c = sqrt(4^2 + 3^2) = sqrt(16 + 9) = sqrt(25) = 5

2. TypeScript custom distance function example

const calculateDistance = (p1: Point, p2: Point): number => {
  const a = p2.x - p1.x;
  const b = p2.y - p1.y;

  return Math.sqrt(a * a + b * b);
};

// Usage example:

interface Point {
  x: number;
  y: number;
}

const p1: Point = { x: 7, y: 2 };
const p2: Point = { x: 3, y: 5 };

const distance: number = calculateDistance(p1, p2);

console.log(distance); // 5

Output:

5

3. Math.hypot() method example

Note: Math.hypot() has been introduced in ECMAScript 2015.

const calculateDistance = (p1: Point, p2: Point): number => {
  const a = p2.x - p1.x;
  const b = p2.y - p1.y;

  return Math.hypot(a, b);
};

// Usage example:

interface Point {
  x: number;
  y: number;
}

const p1: Point = { x: 7, y: 2 };
const p2: Point = { x: 3, y: 5 };

const distance: number = calculateDistance(p1, p2);

console.log(distance); // 5

Output:

5

References

1. Pythagorean equation