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2D Geometry1

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Lakshmikanta Satapathy
Lakshmikanta Satapathy

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.

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Physics Helpline L K Satapathy 2D Geometry 1
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
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
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
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2D Geometry1

  • 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 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