What is the Distance Between Two Points?
The distance between two points is the straight-line length from one point to another. Imagine two locations on a map. If you draw a straight line between them, that is the distance we are talking about.
Mathematically, we use the distance formula to find it:
\[ d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} \]
It’s essentially an application of the Pythagorean theorem, where \(\Delta x = (x_2 – x_1)\) and \(\Delta y = (y_2 – y_1)\). If you’ve taken a basic geometry or algebra class, you’ve likely seen this formula before. Our Distance Calculator automates this entire process for you!
Example Use Case
Suppose you have two points \(A(3, 4)\) and \(B(6, 8)\). Enter the values into the calculator:
\(x_1 = 3,\; y_1 = 4\)
\(x_2 = 6,\; y_2 = 8\)
Hit “Calculate Distance,” and you’ll see:
Distance: \[ (6 – 3)^2 + (8 – 4)^2 = 5.0000 \]
Steps:
- \(\Delta x = 3\) and \(\Delta y = 4\)
- \(3^2 = 9\) and \(4^2 = 16\)
- \(9 + 16 = 25\)
- \(\sqrt{25} = 5\)
You’ll also see a graph with points \(A\) and \(B\) neatly drawn.