The document discusses 2D geometry and provides various mathematical formulae related to the equation of a straight line. Key topics include the point-slope form, slope-intercept form, two-point form, and intercept form with detailed explanations for each. Additionally, it includes formulas for lines parallel and perpendicular to the axes, and mentions related resources for further learning.

1. Physics Helpline
L K Satapathy
2D Geometry 2

2. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
0 0
0
y c
m y c y c
x

       

Line parallel to x-axis at a distance c from it
y = c
O x
y
c
(0, c) A P (x , y)
x=c
c
A (c,0)
P (x , y)
Y - coordinate of every point on the line = c
 Coordinates of A = (0 , c) and let P = (x , y)
1 0 0
0
x c x c x c
m y
       

Line perpendicular to x-axis at a distance c from it
X - coordinate of every point on the line = c
 Coordinates of A = (c , 0) and let P = (x , y)
1 0
m
Slope of AP is not defined ,  we put
Slope of AP is zero ,  we put m = 0
Physics Helpline
L K Satapathy

3. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
1 1( , )x y
Point Slope Form
O x
y
A
P
( , )x y
1 1( , )x y
Given point A = Given slope = m
( , )x yAny point on the line P =
1
1 1
1
( )
y y
m y y m x x
x x

    

Slope of AP =
O x
y
B
P
( , )x y(0, )b
b
Slope Intercept Form
(0, )by-intercept = b  B =
( , )x yAny point on the line P =
Given slope = m
0
y b
m y b mx y mx b
x

      

Slope of BP =
Physics Helpline
L K Satapathy

4. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
1 2 1
1 2 1
AB AC
y y y y
m m
x x x x
 
   
 
O x
y
A
P
B ( , )x y
1 1( , )x y
2 2( , )x y
Two Point Form
Given points A = and B =1 1( , )x y 2 2( , )x y
( , )x yAny point on the line , P =
2 1 1
2 1 1
,AB AC
y y y y
m m
x x x x
 
  
 
2 1
1 1
2 1
( )
y y
y y x x
x x

   

Physics Helpline
L K Satapathy

5. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
1
yx
a b
  
Intercept Form
O A
B
a
b
P ( , )x y
(0, )b
( ,0)a
Given Intercepts : ,OA a OB b 
( ,0) , (0, )A a B b  
Slope of AB
0
0AB
b bm
a a
  

Slope of AP
0
AP
y y
m
x a x a

 
 
( , )x yAny point on the line P =
1AP AB
y yb a x xm m
x a a b a a
       

Physics Helpline
L K Satapathy

6. 2D - GEOMETRY FORMULAE
Equation of a Straight Line
cos sinx y p   
Normal Form
O A
B
a
b
C
p

Given :
,OA a OB b 
( ) ,COA OBC OC p    
Intercepts
In  COA cos
cos
p pOC a
OA a


   
In  OBC sin
sin
p pOC b
OB b


   
1 1
cos sin
y yx x
a b p p 
     
sincos 1
yx
p p
  
Physics Helpline
L K Satapathy

7. Physics Helpline
L K Satapathy
For More details:
www.physics-helpline.com
Subscribe our channel:
youtube.com/physics-helpline
Follow us on Facebook and Twitter:
facebook.com/physics-helpline
twitter.com/physics-helpline