coordinate geometry formulas

Co-ordinate Geometry 1. Distance between two points P and Q = P ( x1 , y1 ) and Q ( x2 , y2 ) 2. The coordinate of the point R ( x, y ) which divides the straight line joining two given points ( x1 , y1 ) and ( x2 , y2 ) internally in a given ratio m1 : m2 is ( x2  x1 )2  ( y2  y1 ) 2  m1 x2  m2 x1 m1 y2  m2 y1  ,   m1  m2   m1  m2 3. Mid-point formula: The coordinates of the middle points R ( x, y ) of the line joining the two given points P ( x1 , y1 ) and Q ( x2 , y2 ) is  x1  x2 y1  y2  ,   2   2 4. Area of a triangle whose vertices are ( x1 , y1 ), ( x2 , y2 ) and ( x3 , y3 ) is  1  ( x1 y2  x2 y1 )  ( x3 y2  x3 y2 )  ( x3 y1  x1 y3 ) 2  x1  1  x2  2  x3   x1 y1   y2  y3   y1  5. The equation of the straight line parallel to y axis and at a distance ' a ' form it is xa 6. Slope or gradient of a line, m  tan  7. Slopes of parallel liens are equal, that is m1  m2 8. The product of the slopes of two perpendicular lines is -1 that is m1  m2  1 9. Equation of a line passing through the origin making angle with the positive direction of x -axis is y  mx 10. The equation of a straight line passing through a point ( x1 , y1 ) and ( x, y ) and having slope m is y  y1  m( x  x1 ) 11. The equation of a straight line passing through a point ( x1 , y1 ) and ( x2 , y2 ) is y  y1  y2  y1 ( x  x1 ) x2  x1 12. The equation of a straight line which cuts off intercepts a and b on the x and x y y axis respectively is   1 a b 13. General equation of a circle is x 2  y 2  2 gx  2 fy  c  0 . Its centre is (  g ,  f ) and radius is g2  f 2  c r is 14. Equation of a circle whose centre is C ( h, k ) and radius ( x  h) 2  ( y  k ) 2  r 2 15. The equation of a circle whose centre is the origin is x 2  y 2  r 2