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Coordinates

Year 7 📐 Geometry & Measures  Plot and read coordinates in all four quadrants.

🗺️ The Coordinate Grid

Coordinates locate a point on a grid using two numbers: $(x, y)$. The $x$-axis is horizontal, the $y$-axis is vertical. Both extend into negative values.

⚡ Remember
Along the corridor, then up the stairs: read $x$ first, then $y$.
Example: Point $(3, -2)$ is 3 units right of the origin and 2 units down.

📏 Midpoint and Distance

You can calculate the midpoint between two points and the straight-line distance between them.

⚡ Midpoint Formula
$$M = \left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)$$
⚡ Distance Formula
$$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$$
Example: Midpoint of $(1, 3)$ and $(5, 7)$: $M = (3, 5)$. Distance $= \sqrt{16+16} = \sqrt{32} = 4\sqrt{2}$

📊 Plotting and Reading Graphs

Coordinates are the foundation for all graph work in algebra and beyond.

💡 Always label your axes and mark a suitable, even scale before plotting points.
Example: Points $(0,1),(1,3),(2,5),(3,7)$ all lie on the line $y = 2x + 1$ — they form a straight line.
🎯 Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
🎬 Interactive Demonstration — Coordinates
Hover over the grid to explore coordinates!
🧮 🗺️ Coordinate Plotter

Enter two points to find the midpoint and distance.