Coordinate Geometry: Class 9 Study Guide
Two number lines at right angles let us give every point an address.
The Cartesian plane has a horizontal line, the x-axis, and a vertical line, the y-axis. They meet at the origin, O(0, 0). A point is written as (x, y). The first number is the abscissa, its distance along the x-axis. The second is the ordinate, its distance along the y-axis.
The axes divide the plane into four quadrants, numbered anticlockwise starting from the top right.
Signs and quadrants
| Quadrant | Sign of x | Sign of y | Example |
|---|---|---|---|
| I | + | + | (3, 2) |
| II | − | + | (−3, 2) |
| III | − | − | (−3, −2) |
| IV | + | − | (3, −2) |
| On the x-axis | any | 0 | (4, 0) |
| On the y-axis | 0 | any | (0, −5) |
Plotting a point
To plot (−2, 3), start at the origin, move 2 units left along the x-axis, then 3 units up, and mark the point. It lies in Quadrant II. The point (3, −2) is not the same as (−2, 3): the order matters, so (x, y) is an ordered pair.
(0, 0).
Right if positive, left if negative.
Up if positive, down if negative.
Write the coordinates.
Shapes from points
Plot (1, 1), (4, 1), (4, 3) and (1, 3) and join them in order. The result is a rectangle 3 units wide and 2 units high. Points with the same x-coordinate lie on a vertical line, and points with the same y-coordinate on a horizontal line.
Worked examples and common mistakes
Example: In which quadrant is (−4, −1)? Quadrant III. Example: What is the distance between (2, 5) and (2, 1) on the same vertical line? 5 − 1 = 4 units. Common mistakes: plotting y before x, forgetting that left and down are negative, and saying that a point on an axis belongs to a quadrant. Points on the axes lie in no quadrant.
Check your understanding: model answers
1. Quadrant IV. 2. On the y-axis, 3 units below the origin. 3. A right-angled triangle with legs of 3 and 4 units.
✨ Key Takeaways
- A point is an ordered pair (x, y).
- The origin is (0, 0).
- Quadrants run anticlockwise from the top right.
- Points on an axis lie in no quadrant.
💬 Questions for Discussion & Reflection
- Write the quadrant of (5, −7).
- Where does (0, −3) lie?
- Plot (2, 2), (5, 2) and (5, 6). What shape do you get when you join them?
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