Q1. In which quadrant does the point (−3, 5) lie?
x = −3 (negative), y = 5 (positive)
Negative x, positive y is Quadrant II
So (−3, 5) lies in Quadrant II.
Coordinate Geometry — Class 9
Every point in a plane has an address — an (x, y) pair. Learn how the Cartesian system fixes any point uniquely.
Cartesian planeTwo perpendicular number lines (x-axis horizontal, y-axis vertical) meeting at the origin O(0,0), dividing the plane into four quadrants.
Abscissa & ordinateFor a point (x, y): x is the abscissa (distance from the y-axis), y is the ordinate (distance from the x-axis).
QuadrantsQuadrant I: (+,+); II: (−,+); III: (−,−); IV: (+,−). Points on an axis belong to no quadrant.
Solved examples
Q2. What are the coordinates of a point 4 units to the left of the y-axis and 2 units below the x-axis?
Left of the y-axis ⇒ x is negative: x = −4
Below the x-axis ⇒ y is negative: y = −2
The point is (−4, −2).
Formula sheet
| Quantity | Formula |
|---|---|
| A point on the x-axis | has y-coordinate = 0 |
| A point on the y-axis | has x-coordinate = 0 |
| Origin | (0, 0) |
Common mistakes & exam wins
- Always read coordinates as (x, y) — x first (horizontal), then y (vertical).
- A point with x = 0 lies ON the y-axis; a point with y = 0 lies ON the x-axis — neither is "in" a quadrant.
- Remember the quadrant signs going anticlockwise from the top right: (+,+), (−,+), (−,−), (+,−).
Frequently asked questions
What are the axes of the Cartesian plane called?
The horizontal line is the x-axis and the vertical line is the y-axis; they meet at the origin.
What is the abscissa and ordinate of a point?
The abscissa is the x-coordinate; the ordinate is the y-coordinate.
How many quadrants does the Cartesian plane have?
Four, numbered I to IV anticlockwise starting from the top right, each with a fixed sign pattern for (x, y).