❖ Learn Plotting Points in a \(3D\) Coordinate System (\(XYZ\)) in this clear, beginner-friendly coordinate geometry lesson!

In this lesson, you’ll learn what the \(3D\) (three-dimensional) coordinate system (\(xyz\)-space) is, how to use the \(x\)-, \(y\)-, and \(z\)-axes that meet at the origin \((0, 0, 0)\), and why plotting a point in \(3D\) requires three values: \((x, y, z)\).

We’ll work through two examples step by step using dashed guide lines:

✅ Example \(1\): \(P(1, 2, 3)\)

✅ Example \(2\): \(P(1, −2, 4)\)

🧭 Direction shortcut:

🔵 →/← for \(x\)-axis (right/left)

🔴 forward/backward for \(y\)-axis

🟢 ↑/↓ for \(z\)-axis (up/down)

📚 Topics Covered:

– What is the \(3D\) coordinate system (\(xyz\)-space)?

– Axes & origin: \(x, y, z\) meeting at \((0,0,0)\)

– From \(1D\) to \(3D\): number line → coordinate plane → \(3D\) space

– Ordered triples \((x, y, z)\) and what each coordinate represents

– How signs control direction: \(x\) right/left, \(y\) forward/backward, \(z\) up/down

– Step-by-step plotting using dashed guide lines

– Practice examples in \(3D\)

🎯 Whether you’re a student, teacher, or math enthusiast, this lesson will help you understand plotting points in \(3D\) simply and clearly.