This document discusses concepts related to 2D geometry including: - Formulas for calculating the distance between two points and the slope of a line joining two points. - Formulas for finding the midpoint, internal and external divisions of a line segment, and the area of a triangle. - Relationships between the slopes of parallel and perpendicular lines and determining if three points are collinear based on slopes.

1. Physics Helpline
L K Satapathy
2D Geometry 1

2. Distance and Slope
Distance between two points and
2 2
2 1 2 1( ) ( )d x x y y   
2 1
2 1
tan
y y
m
x x


 

O

x
y
1 1( , )x y
2 2( , )x y1 1( , )x y 2 2( , )x y
Slope of the line joining two points and
Slope is +ve when 90o
 

1 1( , )x y
2 2( , )x y
Slope is −ve when 90o
 

1 1( , )x y
2 2( , )x y
Physics Helpline
L K Satapathy
1 1( , )x y 2 2( , )x y
2D Geometry 1

3. 1 2 1 2
( , ) ,
2 2
x x y y
x y
  
  
 
1 2 3 2 3 1 3 1 2
1 ( ) ( ) ( )
2
x y y x y y x y y      
2 1 2 1
( , ) ,
mx nx my ny
x y
m n m n
  
    
2 1 2 1
( , ) ,
mx nx my ny
x y
m n m n
  
    
Internal
division
External
division 1 1( , )x y 2 2( , )x y ( , )x y
m
n
1 1( , )x y 2 2( , )x y( , )x y
nm
Mid point
Area of Triangle
A
B C
1 1( , )x y
2 2( , )x y 3 3( , )x y
Section Formula and Area of Triangle
Section Formula : Coordinates of point dividing the join of and
in ratio m : n
1 1( , )x y 2 2( , )x y
Physics Helpline
L K Satapathy
2D Geometry 1

4. Straight Lines and their Slopes
When two lines are parallel [ = 0]
2 1 1 2tan 0 0m m m m      
1m
2m
1m
2m
When two lines are perpendicular [ = 90]
1 2 1 2cot 0 1 0 1m m m m        
Angle between two lines () is given by
2 1
1 2
tan
1
m m
m m




1m
2m

1 1( , )x y 3 3( , )x y2 2( , )x y
A B CABm BCmPoints A , B and C are collinear when
AB BCm m
Physics Helpline
L K Satapathy
2D Geometry 1

5. Physics Helpline
L K Satapathy
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