Coordinate Geometry
Coordinate geometry lets us describe the position of a point using a pair of numbers. This Class 9 chapter introduces the Cartesian plane, its axes and four quadrants, the meaning of abscissa and ordinate, the sign conventions in each quadrant, and how to plot points. It builds the base for the distance and section formulas you will meet in Class 10.
Learning objectives
- Describe the Cartesian plane and its axes.
- Identify the four quadrants and their sign conventions.
- Define abscissa and ordinate.
- Plot a point given its coordinates.
- Locate points on the axes and the origin.
Key concepts
The Cartesian plane
Two perpendicular number lines — the horizontal x-axis and the vertical y-axis — meet at the origin O(0, 0) and divide the plane into four regions called quadrants.
Coordinates, abscissa and ordinate
A point is written as an ordered pair (x, y). The first number x (distance from the y-axis) is the abscissa; the second number y (distance from the x-axis) is the ordinate.
Sign conventions in the quadrants
Quadrant I: (+, +); Quadrant II: (−, +); Quadrant III: (−, −); Quadrant IV: (+, −). A point on the x-axis has y = 0, and a point on the y-axis has x = 0.
Plotting points
To plot (x, y), move x units along the x-axis (right if positive, left if negative), then y units parallel to the y-axis (up if positive, down if negative), and mark the point.
Important formulas
Origin
O = (0, 0)
Point on x-axis
(x, 0)
Point on y-axis
(0, y)
Quadrant signs
I(+,+) II(−,+) III(−,−) IV(+,−)
Key definitions
- Cartesian plane
- A plane formed by two perpendicular number lines, used to locate points.
- Abscissa
- The x-coordinate of a point — its distance from the y-axis.
- Ordinate
- The y-coordinate of a point — its distance from the x-axis.
- Quadrant
- One of the four regions into which the axes divide the plane.
Solved examples
Q1. In which quadrant does the point (−3, 2) lie?
Solution: The x-coordinate is negative and the y-coordinate is positive, so the point lies in Quadrant II.
Q2. Where does the point (4, 0) lie?
Solution: Its y-coordinate is 0, so it lies on the x-axis (4 units to the right of the origin).
Q3. Name the abscissa and ordinate of (7, −5).
Solution: Abscissa = 7 (the x-coordinate); ordinate = −5 (the y-coordinate).
Common mistakes to avoid
- Swapping x and y while writing or plotting a point.
- Mixing up abscissa (x) and ordinate (y).
- Getting the quadrant signs wrong, especially for II and IV.
- Forgetting that points on the axes are not in any quadrant.
Coordinate Geometry — MCQ Quiz
12 questions with instant feedback. Use number keys 1–4 to answer.
The point (3, 4) lies in:
Practice questions
Short answer
What is an ordered pair?
A pair of numbers (x, y) written in a fixed order to locate a point.
Name the quadrant where both coordinates are negative.
Quadrant III.
Where does the point (0, 5) lie?
On the y-axis, 5 units above the origin.
Long answer
Plot the points A(2, 3), B(−2, 3), C(−2, −3) and D(2, −3). What figure do they form?
A is in Quadrant I, B in II, C in III and D in IV. They are symmetric about both axes and form a rectangle (in fact, with these values, a rectangle of width 4 and height 6).
State the sign of the coordinates of a point in each quadrant.
Quadrant I: (+, +); Quadrant II: (−, +); Quadrant III: (−, −); Quadrant IV: (+, −).
HOTS (Higher Order Thinking)
A point lies on the x-axis at a distance of 5 units to the left of the origin. What are its coordinates?
On the x-axis y = 0, and 'left' means negative x, so the point is (−5, 0).
If the abscissa and ordinate of a point are equal and negative, in which quadrant does it lie?
Both negative means Quadrant III (e.g. (−4, −4)).
Quick revision
Revision notes
- Axes meet at origin (0, 0), making four quadrants.
- Point = (abscissa, ordinate) = (x, y).
- Signs: I(+,+), II(−,+), III(−,−), IV(+,−).
- x-axis: y = 0; y-axis: x = 0.
Key takeaways
- Always write coordinates as (x, y) in that order.
- Memorise the quadrant sign pattern.
- Points on the axes belong to no quadrant.
Frequently asked questions
What is the difference between abscissa and ordinate?
The abscissa is the x-coordinate (distance from the y-axis); the ordinate is the y-coordinate (distance from the x-axis).
How many quadrants are there?
Four, numbered I to IV anticlockwise starting from the top-right.
Where is the point (0, 0)?
At the origin, where the x-axis and y-axis intersect.