Chapter 3 · NCERT Class 9 Mathematics

Coordinate Geometry

Every point in a plane can be pinned down by just two numbers. Learn the two axes, the origin, the four quadrants and how to plot and read any point written as an ordered pair (x, y). Tap each term to see exactly what it means.

📐 3 topics⏱ ~25 min📝 12-question quiz

Play with it

The language of the coordinate plane

Coordinate geometry has a precise vocabulary. Tap each term to see what it points to on the plane and how the pieces fit together.

Explore · The coordinate planetap a term

Learn

The three big ideas

The plane is built from two perpendicular number lines: the horizontal x-axis and the vertical y-axis.
The two axes cross at the origin, whose coordinates are (0, 0).
The axes split the plane into four quadrants — I, II, III and IV — counted anticlockwise from the top-right.

The x-coordinate (abscissa) is the first number — how far left/right of the origin. The y-coordinate (ordinate) is the second number — how far up/down.
Sign pattern by quadrant: I (+, +), II (−, +), III (−, −), IV (+, −).

Worked example. In which quadrant does the point (−3, 5) lie?

The x-coordinate is −3 (negative → left of the origin) and the y-coordinate is 5 (positive → above the origin). The sign pattern (−, +) belongs to Quadrant II.

To plot (x, y): start at the origin, move x along the x-axis (right if +, left if −), then move y parallel to the y-axis (up if +, down if −).
To read a point: drop perpendiculars to each axis — the foot on the x-axis gives x, the foot on the y-axis gives y.
Points on the x-axis have y = 0; points on the y-axis have x = 0.

Common mistake: swapping the order in (x, y). The order matters — (2, 3) and (3, 2) are different points: the first lands 2 right & 3 up, the second 3 right & 2 up.

Where you'll meet it

Coordinates, everywhere

Maps & GPS

Latitude and longitude are just coordinates on a giant grid wrapped around the Earth. Your phone's GPS pins your location as a pair of numbers — and any map app plots and reads those points exactly the way you do here.

Computer & phone screens

Every pixel has an (x, y) address measured from a corner of the screen. Games, drawings and even the spot where your finger taps are all located using coordinates.