2D Distance Calculator: Find Distance Between Two Points

What is the Distance Between Two Points?

The distance between two points is like measuring how far apart two places are on a map. It's the length of the straight line that connects these two points.

How to Calculate the Distance Between Two Points

To find the distance between two points, we use their coordinates. It's like following a treasure map where X marks the spot!

Formula

The magic formula for finding the distance between two points (x₁, y₁) and (x₂, y₂) is:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:

• \(d\) is the distance between the two points
• \(x_1, y_1\) are the coordinates of the first point
• \(x_2, y_2\) are the coordinates of the second point
• \(\sqrt{}\) means we take the square root

Calculation Steps

1. Write down the coordinates of your two points
2. Subtract x-coordinates: (x₂ - x₁)
3. Subtract y-coordinates: (y₂ - y₁)
4. Square both differences
5. Add the squared differences
6. Take the square root of the sum

Example and Visual Representation

Let's find the distance between points A(1, 2) and B(4, 6):

Step 1: We have (x₁, y₁) = (1, 2) and (x₂, y₂) = (4, 6)

Step 2: x₂ - x₁ = 4 - 1 = 3

Step 3: y₂ - y₁ = 6 - 2 = 4

Step 4: (x₂ - x₁)² = 3² = 9, (y₂ - y₁)² = 4² = 16

Step 5: 9 + 16 = 25

Step 6: \(\sqrt{25} = 5\)

The distance between A and B is 5 units!

In this picture, you can see our two blue points, A and B. The red line shows the distance between them. The grid helps us see how we count the spaces between the points. Isn't it cool how we can find the exact distance using just the coordinates?