Distance Between Two Points Calculator

This Distance Between Two Points Calculator helps you find the straight-line distance between two points on a coordinate plane. It uses the formula d = √((x₂ − x₁)² + (y₂ − y₁)²), where (x₁, y₁) and (x₂, y₂) are the two points, and the answer is written in units. First find the differences in the x-coordinates and y-coordinates, square them, add them together, and then take the square root. It is a simple way to check answers, understand the distance formula, and practise basic geometry step by step.

Enter the coordinates for (x₁, y₁) and (x₂, y₂).

Step-by-step method

1. Identify what is given.
2. Write the formula.
3. Substitute the values and calculate the distance.

Formula:

Example 1:

Step 1 - Identify what is given.

In this problem: The given points are \((0, 0)\) and \((3, 4)\).

Step 2 - Write the formula.

In this problem: Use the distance formula: \(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\).

Step 3 - Substitute the values and calculate the distance.

In this problem: Compute differences: \(\Delta x = 3 - 0 = 3\) and \(\Delta y = 4 - 0 = 4\). Then \(d = \sqrt{3^{2} + 4^{2}} = \sqrt{25} = 5\).

Final answer:

Example 2:

Step 1 - Identify what is given.

In this problem: The given points are \((-2, 1)\) and \((4, 5)\).

Step 2 - Write the formula.

In this problem: Use the distance formula: \(d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}\).

Step 3 - Substitute the values and calculate the distance.

In this problem: Compute differences: \(\Delta x = 4 - (-2) = 6\) and \(\Delta y = 5 - 1 = 4\). Then \(d = \sqrt{6^{2} + 4^{2}} = \sqrt{52} \approx 7.21\).

Final answer: