Coordinate Geometry

Board: GSEB | Class: Std 9

Comprehensive study notes for Coordinate Geometry by Ajay Yadav (Math King of Katargam). Learn to locate points on a plane using coordinates and understand the Cartesian system.

1. The Cartesian Plane

The Cartesian plane consists of two perpendicular lines:

• X-axis: The horizontal line
• Y-axis: The vertical line
• Origin: The point where X and Y axes intersect (0, 0)

2. Quadrants

The axes divide the plane into four quadrants:

Quadrant	Sign of x	Sign of y	Example
I	+	+	(3, 4)
II	–	+	(-2, 5)
III	–	–	(-3, -1)
IV	+	–	(4, -2)

3. Coordinates of a Point

A point is written as (x, y), where:

• x-coordinate (Abscissa): Distance from the Y-axis
• y-coordinate (Ordinate): Distance from the X-axis

Example: Point (3, -2) means 3 units to the right of origin and 2 units down.

Solved Examples

Example 1: In which quadrant does (-3, 5) lie?

Solution: x = -3 (negative), y = 5 (positive) → Quadrant II

Example 2: Write the coordinates of a point on the x-axis at a distance of 4 units from the origin.

Solution: On the x-axis, y = 0. So point is (4, 0) or (-4, 0)

Practice Questions

1. Plot the points (2, 3), (-1, 4), (-3, -2), (5, -1) on a Cartesian plane. State their quadrants.
2. Find the coordinates of a point whose ordinate is 5 and abscissa is -2.
3. What is the x-coordinate of any point on the y-axis?
4. Name the quadrant where both coordinates are negative.

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