❖ Learn how to find the distance between two points in \(2D\) in this beginner-friendly coordinate geometry lesson!

We explain the distance formula in two dimensions (\(2D\)), why it works (from the Pythagorean Theorem), and how to apply it both algebraically and graphically on the coordinate plane (\(xy\)-plane) all with clear, step-by-step examples.

🎯 Key concepts covered:

– Distance formula in \(2D\):

$$d = \sqrt{(x_2 − x_1)^2 + (y_2 − y_1)^2}$$

– How the formula comes from the Pythagorean Theorem

– Using the horizontal change (\(\Delta x\)) and vertical change (\(\Delta y\)) to form a right triangle on the \(xy\)-plane

– Algebraic vs graphical methods (both give the same result)

– Plotting tips for the coordinate plane (horizontal/vertical changes)

✔️ Important points:

✅ Distance is always non-negative (length)

✅ In \(2D\), you need two values (\(x\)– and \(y\)-coordinates) to locate a point

✅ Squaring differences removes signs; the square root returns the length

✅ The order of the points doesn’t matter, you get the same distance

✔️ What this lesson includes:

– Simple explanation of the distance formula in \(2D\)

– Step-by-step worked examples

– Graphical method using a right triangle with horizontal change (\(\Delta x\)) and vertical change (\(\Delta y\)) on the \(xy\)-plane.

🎯 Whether you’re a student, teacher, or math enthusiast, this lesson will help you understand how to find the distance between two points in \(2D\) and apply the distance formula with confidence!

✨ Watch next:

🔹 Distance between Two Points in \(3D\)