Coordinate (Cartesian) System - Coordinate Geometry
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Neeche(below) teen(three) diagrams/pictures diye gaye hain. Inn diagrams/pictures mein ek rectangle hai jisme ek point P hai. Aapko ye bataana hai ki point P ki rectangle mein kya position hai. Matlab aapko point p ki position bataani hai with respect to the rectangle.
Inn teeno(three) diagrams/pictures ko dekhkar aapko point P ki position ke baare mein kya pata chalta hai? Shaayad aapko teeno(three) diagrams pictures mein point P ki position ke liye ek hai answer mila hoga aur woh yeh hai ki point P rectangle mein upper-right corner mein hai. (Am I right?)
Yaha par hum dekh sakte hain ki teeno(three) diagrams pictures mein ki point P ki position mein kuch na kuch difference hai but sabhi ke liye hamara answer ek hi jaisa hai.
Kehne ka matlab yeh hai ki hum yaha par point P ki position sirf point P aur uske surrounding- jo ki rectangle ka part hai, usse dekh kar bata rahe hain. Hamaare paas aisa koi method/system nahi hai jisse ki hum point P ki position ko accurately measure kar paayein.
To ab sawaal(question) ye hai- Kya koi aisa method nahi jisse hum point P ki position ko accurately bata paayein?
Kuch isi tarah ka sawaal(question) aaj se approx. 400 saal pehle France ke ek philosopher, Rene Descartes ke mind me hit kar raha tha. Aur phir kya hua???....
Aur phir hua Coordinate Geometry ka janm(birth)...
Coordinate geometry ka startup/beginning sabse pehle Rene Descartes ne san 1637 mein kiya tha. Rene Descartes ne Vigyaan(Science) par ek bahut bada granth/book likha tha jisme teen(three) parts/blocks the. Unme se ek part/block Co-ordinate Geometry ka tha. Ussi granth/book mein Coordinate geometry ka use start kiya tha. Doosre shabdo mein kaha jaaye to unhone Geometry mein Algebra ka use kiya tha. Iske pehle mathematicians sirf Euclid ki Geometry tak hi limited the aur unn logo ko ye nahi pata tha ki Geometry se related problems mein Algebra ka use kiya jaa sakta hai. Rene Descartes ne iss granth/book mein explain kiya hai ki kaise kisi plane mein kisi point ki position show ki jaa sakti hai. Aur iss system ko unke naam(name) par aaj bhi Cartesian system kehte hain.
[More to know: Rene Descartes ne hi sabse pehle powers/exponents ko variables ke upar likhne ka rule/system start kiya tha. E.g. x4, x7, y8 etc.].
To chaliye ab aate hain point par...
Coordinate System (Cartesian System)
Kisi plane mein kisi point ki exact position ko bataane ke liye Rene Descartes ek system banaaya jisme do(two) number line hoti hai aur woh dono number lines ek doosre ke perpendicular hoti hain. Aur unn dono number lines ke intersection point ko Origin kehte hain. Isme jo number line horizontal hoti hai usko X-axis aur jo number line vertical hoti hai usko Y-axis kehte hain.
[Agar aapko nahi pata hai ki number line kya hota hai to ye jaanne ke liye iss blue link par click kijiye >>>
Number Line].
Iss system ko Coordinate System ya Cartesian System kehte hain. Isme Origin ke right side ki taraf saare numbers positive (+) hote hain aur Origin ke left side ki taraf saare numbers negative (-) hote hain. Isi tarah se Origin se upar(upward) ki taraf saare numbers positive (+) hote hain aur Origin ke neeche(downward) ki taraf saare numbers negative (-) hote hain.
Chaliye ab dekhte hain ki iss system (Cartesian ya Coordinate System) ka use hum kisi. point ki exact position bataane mein kaise karte hain.
Upar diye gaye diagram mein chaar(four) points diye gaye hain P, Q, R and S. Chaliye ek-ek karke inn sabhi points ki position find karte hain. Cartesian System ya Coordinate System mein kisi point ki position find karne ke liye sabse pehle ye dekhte hain ki wo point X-axis par kaun se number par aata hai aur phir ye dekhaa jaata hai ki wo point Y-axis par kaun se number par aata hai. Example ke liye hame point P ki position find karni hai point P, X-axis par number 2 par hai aur Y-axis par number 1 par aata hai. So point P ki position hai: (2, 1). Kisi point ki position ko Cartesian System(Coordinate System) mein 'coordinates' kehte hain. Yaha par point P ke coordinates hai (2, 1). Kisi point ke coordinates mein jo first number hota hai (yaani jo number X-axis ka hota hai) usko 'abscissa' ya 'x-coordinate' kehte hain aur jo second number par hota hai (yaani jo number Y-axis ka hota hai) usko 'ordinate' ya 'y-coordinate' kehte hain. Iss example mein point P ka abscissa (x-coordinate) 2 hai aur ordinate (y-coordinate) 1 hai.
Isi tarah se point Q ke coordinates (-1, 3/2), point R ke coordinates (-4, 0) aur point S ke coordinates (4, -3) hain.
[Note:
(i) Origin ke coordinates (0, 0) hote hain.
(ii) Jo points X-axis par aate hain unke coordinates (a, 0) ke form mein hote hain jaha par a koi bhi real number ho sakta hai.
(iii) Jo points Y-axis par aate hain unke coordinates (0, b) ke form mein hote hain jaha par b koi bhi real number ho sakta hai.
(iv) Iss Cartesian System (Coordinate System) mein sirf do(two) hi axis (X-axis and Y-axis) hain iss wajah se isko two-dimensional(2-D) System/Geometry/Plane kaha jata hai.
(v) 2-D Cartesian Plane ko X-Y Plane bhi kaha jaata hai].
Friends iss article mein maine aapko Cartesian System (Coordinate System) ka introduction diya hai. Apne agle(next) articles mein hum seekhenge ki kisi Cartesian Plane mein diye gaye do(two) points ke beech ki distance kaise pata karte hain, agar hame unn dono points ke coordinates pata ho. Aur unn articles mein hum section formula (internally and externally), area of triangle, collinear and non-collinear etc. topics par bhi baat karenge. Tab tak ke liye bye! bye! Take care.....!
I hope ki mera ye article aap ko pasand aaya hoga. Agar aap ko mera ye article pasand aaya ho to comment karke hame bata sakte hain.
Read Also:-
[What is Quadratic Equation ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
What is quadratic equation ?].
[How to Solve Quadratic Equation using Algebraic Formulae ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
How to Solve Quadratic Equations using Algebraic Formulae ?].
[How to Solve Quadratic Equation by Middle Term Splitting Method ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
How to Solve Quadratic Equation by Middle Term Splitting Method ?].
[How to Solve Quadratic Equation using Quadratic Formula ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
Aapne is article ko padhkar kya seekha?
CHECK YOUR KNOWLEDGE
Give answers:
Q.1- What is the coordinates of Origin?
Q.2- What are the coordinates of the point lying on X-axis?
Q.3- What are the coordinates of the point lying on Y-axis?
Aap apne answers hame comment ke through bata sakte hain.
THANKS FOR READING THIS BLOG.
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| (i) |
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| (ii) |
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| (iii) |
Inn teeno(three) diagrams/pictures ko dekhkar aapko point P ki position ke baare mein kya pata chalta hai? Shaayad aapko teeno(three) diagrams pictures mein point P ki position ke liye ek hai answer mila hoga aur woh yeh hai ki point P rectangle mein upper-right corner mein hai. (Am I right?)
Yaha par hum dekh sakte hain ki teeno(three) diagrams pictures mein ki point P ki position mein kuch na kuch difference hai but sabhi ke liye hamara answer ek hi jaisa hai.
Kehne ka matlab yeh hai ki hum yaha par point P ki position sirf point P aur uske surrounding- jo ki rectangle ka part hai, usse dekh kar bata rahe hain. Hamaare paas aisa koi method/system nahi hai jisse ki hum point P ki position ko accurately measure kar paayein.
To ab sawaal(question) ye hai- Kya koi aisa method nahi jisse hum point P ki position ko accurately bata paayein?
Kuch isi tarah ka sawaal(question) aaj se approx. 400 saal pehle France ke ek philosopher, Rene Descartes ke mind me hit kar raha tha. Aur phir kya hua???....
Aur phir hua Coordinate Geometry ka janm(birth)...
Coordinate geometry ka startup/beginning sabse pehle Rene Descartes ne san 1637 mein kiya tha. Rene Descartes ne Vigyaan(Science) par ek bahut bada granth/book likha tha jisme teen(three) parts/blocks the. Unme se ek part/block Co-ordinate Geometry ka tha. Ussi granth/book mein Coordinate geometry ka use start kiya tha. Doosre shabdo mein kaha jaaye to unhone Geometry mein Algebra ka use kiya tha. Iske pehle mathematicians sirf Euclid ki Geometry tak hi limited the aur unn logo ko ye nahi pata tha ki Geometry se related problems mein Algebra ka use kiya jaa sakta hai. Rene Descartes ne iss granth/book mein explain kiya hai ki kaise kisi plane mein kisi point ki position show ki jaa sakti hai. Aur iss system ko unke naam(name) par aaj bhi Cartesian system kehte hain.
[More to know: Rene Descartes ne hi sabse pehle powers/exponents ko variables ke upar likhne ka rule/system start kiya tha. E.g. x4, x7, y8 etc.].
To chaliye ab aate hain point par...
Coordinate System (Cartesian System)
Kisi plane mein kisi point ki exact position ko bataane ke liye Rene Descartes ek system banaaya jisme do(two) number line hoti hai aur woh dono number lines ek doosre ke perpendicular hoti hain. Aur unn dono number lines ke intersection point ko Origin kehte hain. Isme jo number line horizontal hoti hai usko X-axis aur jo number line vertical hoti hai usko Y-axis kehte hain.
 |
| Cartesian System (Cartesian Plane) |
[Agar aapko nahi pata hai ki number line kya hota hai to ye jaanne ke liye iss blue link par click kijiye >>>
Number Line].
Iss system ko Coordinate System ya Cartesian System kehte hain. Isme Origin ke right side ki taraf saare numbers positive (+) hote hain aur Origin ke left side ki taraf saare numbers negative (-) hote hain. Isi tarah se Origin se upar(upward) ki taraf saare numbers positive (+) hote hain aur Origin ke neeche(downward) ki taraf saare numbers negative (-) hote hain.
Chaliye ab dekhte hain ki iss system (Cartesian ya Coordinate System) ka use hum kisi. point ki exact position bataane mein kaise karte hain.
 |
| Cartesian System (Cartesian Plane) |
Upar diye gaye diagram mein chaar(four) points diye gaye hain P, Q, R and S. Chaliye ek-ek karke inn sabhi points ki position find karte hain. Cartesian System ya Coordinate System mein kisi point ki position find karne ke liye sabse pehle ye dekhte hain ki wo point X-axis par kaun se number par aata hai aur phir ye dekhaa jaata hai ki wo point Y-axis par kaun se number par aata hai. Example ke liye hame point P ki position find karni hai point P, X-axis par number 2 par hai aur Y-axis par number 1 par aata hai. So point P ki position hai: (2, 1). Kisi point ki position ko Cartesian System(Coordinate System) mein 'coordinates' kehte hain. Yaha par point P ke coordinates hai (2, 1). Kisi point ke coordinates mein jo first number hota hai (yaani jo number X-axis ka hota hai) usko 'abscissa' ya 'x-coordinate' kehte hain aur jo second number par hota hai (yaani jo number Y-axis ka hota hai) usko 'ordinate' ya 'y-coordinate' kehte hain. Iss example mein point P ka abscissa (x-coordinate) 2 hai aur ordinate (y-coordinate) 1 hai.
Isi tarah se point Q ke coordinates (-1, 3/2), point R ke coordinates (-4, 0) aur point S ke coordinates (4, -3) hain.
[Note:
(i) Origin ke coordinates (0, 0) hote hain.
(ii) Jo points X-axis par aate hain unke coordinates (a, 0) ke form mein hote hain jaha par a koi bhi real number ho sakta hai.
(iii) Jo points Y-axis par aate hain unke coordinates (0, b) ke form mein hote hain jaha par b koi bhi real number ho sakta hai.
(iv) Iss Cartesian System (Coordinate System) mein sirf do(two) hi axis (X-axis and Y-axis) hain iss wajah se isko two-dimensional(2-D) System/Geometry/Plane kaha jata hai.
(v) 2-D Cartesian Plane ko X-Y Plane bhi kaha jaata hai].
Friends iss article mein maine aapko Cartesian System (Coordinate System) ka introduction diya hai. Apne agle(next) articles mein hum seekhenge ki kisi Cartesian Plane mein diye gaye do(two) points ke beech ki distance kaise pata karte hain, agar hame unn dono points ke coordinates pata ho. Aur unn articles mein hum section formula (internally and externally), area of triangle, collinear and non-collinear etc. topics par bhi baat karenge. Tab tak ke liye bye! bye! Take care.....!
I hope ki mera ye article aap ko pasand aaya hoga. Agar aap ko mera ye article pasand aaya ho to comment karke hame bata sakte hain.
Read Also:-
[What is Quadratic Equation ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
What is quadratic equation ?].
[How to Solve Quadratic Equation using Algebraic Formulae ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
How to Solve Quadratic Equations using Algebraic Formulae ?].
[How to Solve Quadratic Equation by Middle Term Splitting Method ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
How to Solve Quadratic Equation by Middle Term Splitting Method ?].
[How to Solve Quadratic Equation using Quadratic Formula ? – iss post ko padhe ke liye iss blue link par click kijiye »»»
Aapne is article ko padhkar kya seekha?
CHECK YOUR KNOWLEDGE
Give answers:
Q.1- What is the coordinates of Origin?
Q.2- What are the coordinates of the point lying on X-axis?
Q.3- What are the coordinates of the point lying on Y-axis?
Aap apne answers hame comment ke through bata sakte hain.
THANKS FOR READING THIS BLOG.
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