Recall Distance between two points Distance between two points A x y ( , and B x y ( , is AB . Mid-point of line segment The mid-point M , of the line segment joining A x y ( , and B x y ( , is x Section Formula Internal Division Let A ( , and B ( , be two distinct points such that point P x y ( , ) divides AB internally in the ratio m:n . Then the coordinates of P are given by mx nx m my ny m External Division Let A ( , and B ( , be two distinct points such that the point P x y ( , ) divides AB externally in the ratio m:n . Then the coordinates of P are given by mx nx m my ny m Centroid of a triangle The coordinates of the centroid G of a triangle with vertices A ( , , B ( , and C ( are given by x Fig.
. A( x , y ) B( x , y ) Fig. . A( x , y ) B( x , y ) M A( x , y ) B( x , y ) m P Fig.
. A( x , y ) B( x , y ) P( x,y ) m Fig. . B( x , y ) C( x , y ) G A( x , y ) Fig.
. Coordinate Geometry Progress Check . Complete the following table. S.No.
Points Distance Mid Point Internal External Point Ratio Point Ratio (i) ( , ), ( , ) : : (ii) (– , ),(– , ) (– , ) . A ( , ), B ( , ) and C ( are vertices of a triangle then its centroid will be at .