❖ Learn how to find the distance between two points in \(3D\) space. We’ll calculate the distance between two points using the distance formula and then build the formula visually step by step.

📌 Distance Formula (\(3D\))

If \(P_1=(x_1, y_1, z_1)\) and \(P_2=(x_2, y_2, z_2)\), then:

$$d = \sqrt{(x_2 − x_1)^2 + (y_2 − y_1)^2 + (z_2 − z_1)^2}$$

SSo, the distance between two points in \(3D\) is the square root of the sum of the squares of the differences in \(x, y,\) and \(z\).

💡 Key Idea

The \(3D\) distance formula comes from applying the Pythagorean Theorem twice, first in the \(xy\)-plane, then using the \(z\)-direction.

🧭 Direction shortcut:

🔵 \(x\): + →, − ←

🔴 \(y\): + forward, − backward

🟢 \(z\): + ↑, − ↓

✅ Perfect for students learning coordinate geometry with clear steps and easy visual explanations.