Straight line k question tricks

Straight line ka equation (saral rekha ka samikaran) tricks se kaise nikalte hai ?

 Hello friends , aaj mai aapk liye ek new mathematics tricks laya hu. Mathematics me ek lesson hai jiska naam hai, straight line aapne jarur suna hoga. Isse hindi me saral rekha kahate hai. Ye lesson mujhe very difficult lagata tha.Aaj mai issi k ek question ko tricks se lagana bataunga. 

Saral rekha ka samikaran-:

Saral rekha ka samikaran nikalane kai type k question hai. Mai aapko " two bindu (two points )" se hokar jane wale line ka equation tricks se nikalana shikhauga. Aayiye dekhte hai

Ques-1. Two points (8,16) and (6,-1) se hokar jane wali line ka equation ?

General method -:

General method se lagane k liye hum two points se hokar jane wali line ka formula lagana padega. Formula ye hai ki two points (x' ,y')and (x'' ,y")se hokar jane wali rekha(line) ka samikaran hai -:

                   Y-y'=[(y"-y')/(x"-x')](x-x')

Ab iss ques me x'=8 , y'=16, x"=6 and y"= -1 hai ye sabhi value ko formula me rakhane par-:

               y-16=[(-1-16)/(6-8)](x-8)

               y-16=[-17/-2](x-8)

               2(y-16)=17(x-8)

               2y-32=17x-136
               17x -  2y=104  answer. 

Tricks -:   

Tricks se karne k liye bas aap nichee diya formula yaad rakhe -:

   ......x-......y=......

Uppar diye formula me "x" aor "y" k left side ko fill kark hum aasani se equation ko nikal sakte hai. Ab " x" aor " y" k pahale and "=" k baad jo fill karna hai usk liye steps ko follow karee-:

Step-1. Formula me "x" k left side = y'-y"

Step-2.Formula me "y" k left side= x'-x"

Step -3.Formula me "=" k right side k liye = (y'x"-x'x")

Ab two points (8,16) and (6,-1) me
x'=8 , y'=16 , x"=6 , and y"= -1
ab formula -:        ......x - ......y = ......
X k left side= y'-y"
                     =16-(-1)=17
Y k left side = x'-x"
                      = 8-6=2
Ab "=" k right side k liye= y'x"-x'x"
                                        = 96-(-8)=104
Sabhi value ko formula me rakhane par -:
17x-2y=104  answer.
To dekha aapne tricks se ye ques Kitna jaldi oar aasani se solve ho gaya. Aayiye kuch oar example dekhte hai-:

Example -1. Two points (1,0) and (0,1) se pass karne wali line ka equation find Karna hai? 

Tricks -: iss me x'=1,y'=0,x"=0,y"=1  
   formula -  ......x - ......y=......

x k left side = y'-y"=0-1=-1

y k left side =x'-x"=1-0=1

= K left side = y'x"-x'y"=0-1=-1

Formula me sabhi value rakhne par - 

-x-y=-1 ya x+y=1 answer. 

Example -2. Two points (-4,5) & (-5,7)

Tricks -: x'=-4,y'=5,x"=-5 and y"=7 formula ...x-...y=...

x k left = 5-7=-2

y k left = -4-(-5)=-4+5=1

"=" k left =5(-5)-(-4)7=-25-(-28)=-25+28=3

Sabhi value formula me rakhne par -:
-2x-1y=3 or 2x+y=3  answer.

Example -3. (3,-4) and (5,-7) 

Tricks-:  formula ...x - ... y=......

x'=3,y'=-4,x"=5 and y"=-7 

x k left =-4-(-7)=3

y k left =3-5=-2

"=" K right = (-4)5-(3)(-7)=1

Formula me sabhi value rakhne -:

3x-(-2)y=1 or 3x+2y=1 answer. 

Example -4.  (3,4) and (-2,5)

Trick -: formula -:  ...x - ...y=......

x k left side -: 4-5=-1
y k left k side-: 3-(-2)=5
"=" k right side-: 4(-2)-(3)5=-23
formula me sabhi value -:
-1x-5y=-23 or x+5y=23 aanswer.

Bas aaj k liye itana hi next post me phir milte hai.aapko ye post kaisa laga? ,ye batana mat bhuliyega. Agar aapko koi problem ho iss article ko samjhne me to mujhse jarur puchhe. Mujhe aapk comments ka intjaar rhega.
 Thank you !