Formulas and concepts in Coordinate Geometry for Class 9 Mathematics: 1. Basics of Coordinate Geometry Coordinate Plane : The coordinate plane consists of two perpendicular lines: X-axis : The horizontal axis. Y-axis : The vertical axis. Origin : The point where the X-axis and Y-axis intersect, denoted as ( 0 , 0 ) (0, 0) ( 0 , 0 ) . Coordinates : Any point on the plane is represented by an ordered pair ( x , y ) (x, y) ( x , y ) , where: x x x is the abscissa (horizontal distance from the Y-axis). y y y is the ordinate (vertical distance from the X-axis). 2. Distance Formula Purpose : To find the distance between two points ( x 1 , y 1 ) (x_1, y_1) ( x 1 , y 1 ) and ( x 2 , y 2 ) (x_2, y_2) ( x 2 , y 2 ) . Formula : d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} 3. Section Formula Purpose : To find the coordinates of a point P ( x , y ) P(x, y) P ( x , y ) dividing a line segment joining points A ( x 1 , y 1 ) A(x_1, y_1) A ( x 1 , y 1 )...