CBSE Class 9 Maths — Ganita Manjari
Chapter 1: Orienting Yourself — The Use of Coordinates
Cheat Sheet · Active Recall Questions · Answer Key
CHEAT SHEET
1. The Coordinate Plane
A coordinate plane is formed by two perpendicular number lines: a horizontal line called the x-axis and a
vertical line called the y-axis. The point where they cross is called the origin, written as O(0, 0). Together,
the two axes are called the coordinate axes, and the plane they form is called the Cartesian plane, named
after the mathematician René Descartes.
2. Locating a Point: Ordered Pairs
Every point on the plane is located using an ordered pair (x, y). The first value, x, is called the abscissa — it
tells you the distance of the point from the y-axis (measured along the x-axis). The second value, y, is called
the ordinate — it tells you the distance of the point from the x-axis (measured along the y-axis). The order
matters: (3, 5) and (5, 3) are different points.
3. The Four Quadrants
The two axes divide the plane into four regions called quadrants, numbered I to IV in anticlockwise order
starting from the top-right.
Quadrant Sign of x Sign of y Example point
I + + (4, 3)
II - + (-4, 3)
III - - (-4, -3)
IV + - (4, -3)
4. Points on the Axes (Special Cases)
● Any point on the x-axis has its y-coordinate equal to 0, e.g. (5, 0), (-2, 0).
● Any point on the y-axis has its x-coordinate equal to 0, e.g. (0, 5), (0, -2).
● The origin is the only point common to both axes: (0, 0).
5. Key Vocabulary at a Glance
Term Meaning
Abscissa x-coordinate; distance from the y-axis
Ordinate y-coordinate; distance from the x-axis
Origin The point (0, 0) where both axes meet
Quadrant One of the 4 regions formed by the two axes
Common Mistakes to Avoid
Chapter 1: Orienting Yourself — The Use of Coordinates
Cheat Sheet · Active Recall Questions · Answer Key
CHEAT SHEET
1. The Coordinate Plane
A coordinate plane is formed by two perpendicular number lines: a horizontal line called the x-axis and a
vertical line called the y-axis. The point where they cross is called the origin, written as O(0, 0). Together,
the two axes are called the coordinate axes, and the plane they form is called the Cartesian plane, named
after the mathematician René Descartes.
2. Locating a Point: Ordered Pairs
Every point on the plane is located using an ordered pair (x, y). The first value, x, is called the abscissa — it
tells you the distance of the point from the y-axis (measured along the x-axis). The second value, y, is called
the ordinate — it tells you the distance of the point from the x-axis (measured along the y-axis). The order
matters: (3, 5) and (5, 3) are different points.
3. The Four Quadrants
The two axes divide the plane into four regions called quadrants, numbered I to IV in anticlockwise order
starting from the top-right.
Quadrant Sign of x Sign of y Example point
I + + (4, 3)
II - + (-4, 3)
III - - (-4, -3)
IV + - (4, -3)
4. Points on the Axes (Special Cases)
● Any point on the x-axis has its y-coordinate equal to 0, e.g. (5, 0), (-2, 0).
● Any point on the y-axis has its x-coordinate equal to 0, e.g. (0, 5), (0, -2).
● The origin is the only point common to both axes: (0, 0).
5. Key Vocabulary at a Glance
Term Meaning
Abscissa x-coordinate; distance from the y-axis
Ordinate y-coordinate; distance from the x-axis
Origin The point (0, 0) where both axes meet
Quadrant One of the 4 regions formed by the two axes
Common Mistakes to Avoid
