🔹 1. What is Coordinate Geometry?
Simple Meaning
Coordinate Geometry helps us find the exact position of a point on a plane using numbers.
সহজ ভাষাত:
Coordinate Geometry ৰ সহায়ত আমি এখন সমতলত (paper) ক’ত এটা বিন্দু আছে তাক সংখ্যা ব্যৱহাৰ কৰি বুজো।
🔹 2. Cartesian Plane
The plane used in coordinate geometry is called the Cartesian Plane.
ইয়াক Cartesian Plane কোৱা হয়।
It has:
- One horizontal line → x-axis
- One vertical line → y-axis
These two lines cross at a point called Origin (0,0).
🔹 3. Axes
(a) X-axis
- Horizontal line
- Right side → positive (+)
- Left side → negative (−)
(b) Y-axis
- Vertical line
- Upwards → positive (+)
- Downwards → negative (−)
🔹 4. Origin
The point where x-axis and y-axis meet is called Origin.
Coordinates of origin = (0, 0)
🔹 5. Coordinates of a Point
Meaning
Coordinates are written as (x, y)
- x → distance from y-axis
- y → distance from x-axis
সহজকৈ:
আগে x, তাৰপিছত y
Example:
Point A (3, 2)
→ Go 3 steps right, then 2 steps up
🔹 6. Quadrants
The x-axis and y-axis divide the plane into 4 parts, called Quadrants.
| Quadrant | Sign of x | Sign of y |
|---|---|---|
| I | + | + |
| II | − | + |
| III | − | − |
| IV | + | − |
📌 Origin is not in any quadrant
🔹 7. Plotting a Point (Step-by-Step)
Example: Plot (−2, 3)
- Start from origin
- Move 2 steps left (−x)
- Move 3 steps up (+y)
- Mark the point
🔹 8. Points on Axes
- If y = 0 → point lies on x-axis
Example: (4, 0) - If x = 0 → point lies on y-axis
Example: (0, −3)
🔹 9. Reading Coordinates from Graph
Easy Rule:
- Draw a straight line down to x-axis → read x
- Draw a straight line to y-axis → read y
🔹 10. Important Exam Points ⭐
✔ Coordinates are always written as (x, y)
✔ First x, then y
✔ Origin = (0, 0)
✔ Quadrants sign rule is very important
🔹 11. Common Mistakes ❌
❌ Writing (y, x) instead of (x, y)
❌ Wrong quadrant sign
❌ Counting boxes wrongly
🔁 One-Line Revision
- Horizontal → x-axis
- Vertical → y-axis
- Meeting point → origin
- Position → coordinates