Finding distance between two points in a 2-D plane using JavaScript

Problem

We are required to write a JavaScript function that takes in two objects both having x and y property specifying two points in a plane.

Our function should find and return the distance between those two points using the Euclidean distance formula.

Distance Formula

The distance between two points (x?, y?) and (x?, y?) is calculated using:

distance = ?[(x? - x?)² + (y? - y?)²]

Example

Following is the code:

const a = {x: 5, y: -4};
const b = {x: 8, y: 12};

const distanceBetweenPoints = (a = {}, b = {}) => {
    let x1 = a.x,
        x2 = b.x,
        y1 = a.y,
        y2 = b.y;
    
    // Apply distance formula: ?[(x?-x?)² + (y?-y?)²]
    let distance = Math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2);
    return distance;
};

console.log(distanceBetweenPoints(a, b));

Output

16.278820596099706

Step-by-Step Calculation

Let's break down the calculation for points a(5, -4) and b(8, 12):

const a = {x: 5, y: -4};
const b = {x: 8, y: 12};

console.log("Point A:", a);
console.log("Point B:", b);
console.log("Difference in x:", b.x - a.x);
console.log("Difference in y:", b.y - a.y);
console.log("(x? - x?)²:", (b.x - a.x) ** 2);
console.log("(y? - y?)²:", (b.y - a.y) ** 2);
console.log("Sum:", (b.x - a.x) ** 2 + (b.y - a.y) ** 2);
console.log("Distance:", Math.sqrt((b.x - a.x) ** 2 + (b.y - a.y) ** 2));

Point A: { x: 5, y: -4 }
Point B: { x: 8, y: 12 }
Difference in x: 3
Difference in y: 16
(x? - x?)²: 9
(y? - y?)²: 256
Sum: 265
Distance: 16.278820596099706

Simplified Version

Here's a more concise version of the function:

const distanceBetweenPoints = (p1, p2) => {
    return Math.sqrt((p2.x - p1.x) ** 2 + (p2.y - p1.y) ** 2);
};

// Test with different points
console.log(distanceBetweenPoints({x: 0, y: 0}, {x: 3, y: 4})); // 5
console.log(distanceBetweenPoints({x: 1, y: 1}, {x: 4, y: 5})); // 5

5
5

Conclusion

The distance between two points is calculated using the Euclidean distance formula with Math.sqrt() and exponentiation. This formula is fundamental in coordinate geometry and many programming applications.