COORDINATE GEOMETRY | SECTION FORMULA, SOME APPLICATIONS OF SECTION FORMULA | The coordinates of the point which divides the line segment joining the points `(x_1;y_1)` and `(x_2;y_2)` internally in the ratio m:n are given by `(x=(mx_2+nx_1)/(m+n);y=(my_2+ny_1)/(m+n))`, (i) Find the coordinates of the point which divides the line segment joining the points (6;3) and (-4;5) in the ratio 3:2 internally, (iv) The three vertices of a parallelogram are taken in order (-1;0); (3;1) and (2;2) respectively. Find the coordinates of 4th vertex., (ii)In what ratio does the x axis divide the line segment joining the points `(2;-3) and (5;6)`. Find the coordinate of a point of intersection, (iii)Prove that the points (-2;-1) ; (1;0);(4;3) and (1;2) are the vertices of the parallelogram . Is this a rectangle ?, Theorem: Prove that the coordinates of centroid of the triangle whose coordinates are `(x_1;y_1);(x_2;y_2) and (x_3;y_3)` are `((x_1+x_2+x_3)/3;(y_1+y_2+y_3)/3)`, If the coordinates of the midpoints of the sides of a triangle are (1;1);(2;-3) and (3;4). Find its centroid.