Introduction: The Crossroads 🚦
Imagine karo tum ek shehar (city) mein ho jahan do main roads ek dusre ko cross karti hain.
- Ek road jo Left-Right jaati hai (Sleeping line).
- Ek road jo Top-Bottom jaati hai (Standing line).
Jahan ye dono roads milti hain, wo shehar ka center point hai.
Coordinate Geometry mein bhi yehi hota hai. Humare paas Do Number Lines hoti hain:
- Ek number line ko hum Horizontal (leta hua) rakhte hain — X-axis.
- Dusri number line ko hum Vertical (khada) rakhte hain — Y-axis.
Jab ye dono lines apne Zeroes (0) par ek dusre ko 90 degree par kat-ti hain, toh humein milta hai Cartesian Plane.
🔑 Important Terms
In terms ko yaad rakhna bahut zaroori hai:
1. X-Axis (Kshitij Rekha)
Ye wo Horizontal Number Line (leti hui line) hai. Right side positive numbers (+), Left side negative numbers (-).
2. Y-Axis (Udharvadhar Rekha)
Ye wo Vertical Number Line (khadi line) hai. Upar positive numbers (+), Neeche negative numbers (-).
3. Origin (Mool-Bindu)
Wo point jahan X aur Y axes ek dusre ko cut karte hain (Zeroes cross here). Iske coordinates hamesha (0, 0) hote hain.
📏 Samjhein Coordinates Ko: (x, y)
Kisi bhi point ki position ko hum ek pair (x, y) se dikhate hain. Order matter karta hai!
📌 Terminology (Yaad Rakhein):
- x-coordinate ko Abscissa (Bhuj) kehte hain.
- y-coordinate ko Ordinate (Koti) kehte hain.
Coordinates As Distances
Ye concept bahut important hai. Dhyan se samjhein:
- x-coordinate (Abscissa): Point ka Y-axis se perpendicular distance. (Hum y-axis se kitna right ya left gaye).
- y-coordinate (Ordinate): Point ka X-axis se perpendicular distance. (Hum x-axis se kitna upar ya neeche gaye).
⚠ Warning: Order Matters!
(3, 4) aur (4, 3) same nahi hain!
- (3, 4) ka matlab: x=3, y=4.
- (4, 3) ka matlab: x=4, y=3.
Isliye isse Ordered Pair kaha jata hai.
4️⃣ Quadrants (Char Hissay)
Jab do lines ek dusre ko cross karti hain, toh wo plane ko 4 parts mein divide karti hain. Har part ko hum Quadrant kehte hain.
Hum Quadrants ko Anti-Clockwise (ghadi ki ulti disha mein) count karte hain, starting from Top-Right.
📝 Sign Convention (Yaad Rakhein):
- Quadrant I: (+, +) → Dono positive.
- Quadrant II: (-, +) → X negative, Y positive.
- Quadrant III: (-, -) → Dono negative.
- Quadrant IV: (+, -) → X positive, Y negative.
📌 Aage Ka Content (Coming Next)
Ab humein system samajh aa gaya hai. Next lesson mein hum seekhenge ki actually mein points ko kaise plot karte hain.