Coordinate Geometry Notes
Coordinate geometry connects algebra and geometry by fixing the position of a point using a pair of numbers. This chapter introduces the Cartesian plane, the x-axis and y-axis, the origin, quadrants, coordinates of a point, and plotting points from an ordered pair.
- 3 min read
- 12 practice questions
- Aligned to CBSE 2025–26 syllabus
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- Updated Sept 2026
Use this map for a first read, then return to the checks and formulas during revision.
- 1.The Cartesian Plane
- 2.Signs of Coordinates in the Quadrants
- 3.Plotting Points and Reading Coordinates
- 1 concept checks
The Cartesian Plane
Two perpendicular number lines — the horizontal x-axis and the vertical y-axis — meet at a point called the origin, O. Together they form the Cartesian plane (coordinate plane). The axes divide the plane into four regions called quadrants, numbered I to IV anticlockwise starting from the upper right.
The position of any point is given by an ordered pair (x, y). The first number x is the x-coordinate or abscissa (distance from the y-axis, positive to the right). The second number y is the y-coordinate or ordinate (distance from the x-axis, positive upward).
Order matters: (3, 5) and (5, 3) are different points.
Signs of Coordinates in the Quadrants
In Quadrant I both coordinates are positive (+, +). In Quadrant II, x is negative and y is positive (−, +). In Quadrant III both are negative (−, −). In Quadrant IV, x is positive and y is negative (+, −).
A point on the x-axis has y = 0, so it looks like (a, 0). A point on the y-axis has x = 0, so it looks like (0, b). The origin is (0, 0). Points lying on the axes are not counted in any quadrant.
So you can tell a point's quadrant just from the signs of its coordinates, without plotting it.
Plotting Points and Reading Coordinates
To plot (x, y): start at the origin, move x units along the x-axis (right if positive, left if negative), then move y units parallel to the y-axis (up if positive, down if negative), and mark the point.
To read the coordinates of a marked point, drop a perpendicular to the x-axis to get the abscissa and a perpendicular to the y-axis to get the ordinate.
Points with the same x-coordinate lie on a vertical line; points with the same y-coordinate lie on a horizontal line. For example, (2, 1), (2, 4), (2, −3) all lie on the vertical line x = 2.
Coordinate Geometry: revision sheet
Close the notes and explain each idea in your own words. Then check the formulas and attempt the examples before opening their solutions.
Recall checklist
- The Cartesian Plane
- Signs of Coordinates in the Quadrants
- Plotting Points and Reading Coordinates
For each topic: state the rule, explain when it applies, give an example and identify one mistake to avoid. Return to any topic you cannot explain without looking.
Explain your method
Write the given information, choose a method, show the steps, then check units and whether the answer makes sense.
Check worked solution 1
Check worked solution 2
Turn mistakes into revision
Record the question, the step that went wrong and the corrected reason. Try it again tomorrow without the solution, then revisit it after a week. A correct guess still needs an explanation.
Practice and Revision
Test your understanding with quick chapter-level practice.
Chapter Q&A
Why is (x, y) called an ordered pair?
Because the order of the numbers matters: the first number is always the x-coordinate and the second is always the y-coordinate. (2, 5) and (5, 2) represent different points.
Do points on the axes belong to a quadrant?
No. Points on the x-axis or y-axis (including the origin) lie on the boundary and are not counted in any of the four quadrants.
How do you know the quadrant of a point without plotting it?
Look only at the signs of its coordinates: (+, +) is I, (−, +) is II, (−, −) is III, (+, −) is IV.
What is the perpendicular distance of the point (5, −3) from the x-axis and from the y-axis?
Distance from the x-axis is |y| = 3 units; distance from the y-axis is |x| = 5 units.