A ( 2 , 5 ) , B ( - 1 , 2 ) and C ( 5 , 8 ) are the vertices of a triangle ABC ' M is a point on AB such that AM : MB = 1 : 2 . Find the coordinates of ' M . Hence find the equation of the line passing through the points C and M .

From the given information we can draw the diagram as: As A M : M B = 1 : 2 and the coordinates of A ( 2 , 5 ) and B ( - 1 , 2 ) Applying section formula we get the coordinates of point M : 1 × - 1 + 2 × 2 1 + 2 , 1 × 2 + 2 × 5 1 + 2 = 3 3 , 12 3 = ( 1 , 4 ) Now applying the two point form to find the equation of the line C M = y - 4 x - 1 = 5 - 1 8 - 4 ⇒ y - 4 x - 1 = 1 ⇒ y - 4 = x - 1 ⇒ y = x + 3 Hence, the coordinates of M = ( 1 , 4 ) and equation of line C M is y = x + 3 .